Elliptic curve isogeny class with Cremona label 32370bg (LMFDB label 32370.bj)

• Label: 32370bg
• Number of curves: $2$
• Conductor: $32370$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 32370bg have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(13\)	\(1 + T\)
\(83\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 32370bg do not have complex multiplication.

Modular form 32370.2.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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 32370bg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
32370.bj2	32370bg1	\([1, 0, 0, -286625, 137015625]\)	\(-2604150083359733274001/6605854145280000000\)	\(-6605854145280000000\)	\([7]\)	\(812224\)	\(2.2990\)	\(\Gamma_0(N)\)-optimal
32370.bj1	32370bg2	\([1, 0, 0, -39869525, -100494513555]\)	\(-7008852130127189520580731601/306494452230385793968620\)	\(-306494452230385793968620\)	\([]\)	\(5685568\)	\(3.2720\)