  Having two "sibling" Type Ia supernovae (SNe Ia) in the same galaxy offers
additional advantages in reducing a variety of systematic errors involved in
estimating the Hubble constant, $H_{0}$. NGC 4414 is a nearby galaxy included
in the Hubble Space Telescope Key Project to measure its distance using Cepheid
variables. It hosts two sibling SNe Ia: SN 2021J and SN 1974G. This provides
the opportunity to improve the precision of the previous estimate of $H_{0}$,
which was based solely on SN 1974G. Here we present new optical $BVRI$
photometry obtained at the Observatorio de Sierra Nevada and complement it with
Swift UVOT $UBV$ data, which cover the first 70 days of emission of SN 2021J. A
first look at SN 2021J optical spectra obtained with the Gran Telescopio
Canarias (GTC) reveals typical SN type Ia features. The main SN luminosity
parameters for the two sibling SNe are obtained by using SNooPy, a light curve
fitting code based on templates. Using a hierarchical bayesian approach, we
build the Hubble diagram with a sample of 96 SNe Ia obtained from the Combined
Pantheon Sample in the redshift range $z = 0.02-0.075$, and calibrate the zero
point with the two sibling type-Ia SNe in NGC 4414. We report a value of the
Hubble constant $H_{0}$ $= 72.19 \pm 2.32$ (stat.) $\pm 3.42$ (syst.) km
s$^{-1}$Mpc$^{-1}$. We expect a reduction of the systematic error after a new
analysis of the Cepheids period-luminosity relation using the upcoming Gaia DR4
and additional Cepheids from the HST and JWST.
