Elliptic curve isogeny class with Cremona label 1400m (LMFDB label 1400.i)

• Label: 1400m
• Number of curves: $1$
• Conductor: $1400$
• CM: no
• Rank: $1$

Rank

The elliptic curve 1400m1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 8 T + 17 T^{2}\)	1.17.ai
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 7 T + 23 T^{2}\)	1.23.h
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 1400m do not have complex multiplication.

Modular form 1400.2.a.m

Isogeny graph

Elliptic curves in class 1400m

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1400.i1	1400m1	\([0, 1, 0, -4208, -106912]\)	\(-10303010/49\)	\(-39200000000\)	\([]\)	\(1440\)	\(0.88219\)	\(\Gamma_0(N)\)-optimal