Elliptic curve isogeny class with Cremona label 361416bg (LMFDB label 361416.bg)

• Label: 361416bg
• Number of curves: $2$
• Conductor: $361416$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 361416bg have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(11\)	\(1 - T\)
\(37\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 361416bg do not have complex multiplication.

Modular form 361416.2.a.bg

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 361416bg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
361416.bg1	361416bg1	\([0, 1, 0, -80757237899, 8833218531981030]\)	\(1418854149881269000523696128/21413352213\)	\(879052852449803089872\)	\([2]\)	\(764854272\)	\(4.4992\)	\(\Gamma_0(N)\)-optimal
361416.bg2	361416bg2	\([0, 1, 0, -80757162604, 8833235827152176]\)	\(-88678136326676754811067728/344501617579257699\)	\(-226277605930577953008863460096\)	\([2]\)	\(1529708544\)	\(4.8458\)