Elliptic curve isogeny class with LMFDB label 21312.a (Cremona label 21312bx)

• Label: 21312.a
• Number of curves: $1$
• Conductor: $21312$
• CM: no
• Rank: $1$

Rank

The elliptic curve 21312.a1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(13\)	\( 1 + 3 T + 13 T^{2}\)	1.13.d
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(23\)	\( 1 - 9 T + 23 T^{2}\)	1.23.aj
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 21312.a do not have complex multiplication.

Modular form 21312.2.a.a

Elliptic curves in class 21312.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
21312.a1	21312bx1	\([0, 0, 0, -105014892, 414216952400]\)	\(-670206957616537490521/6109179936768\)	\(-1167482466835856621568\)	\([]\)	\(3815424\)	\(3.2070\)	\(\Gamma_0(N)\)-optimal