Elliptic curve isogeny class with LMFDB label 245.a (Cremona label 245a)

• Label: 245.a
• Number of curves: $1$
• Conductor: $245$
• CM: no
• Rank: $1$

Rank

The elliptic curve 245.a1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T + 2 T^{2}\)	1.2.c
\(3\)	\( 1 + 3 T + 3 T^{2}\)	1.3.d
\(11\)	\( 1 - T + 11 T^{2}\)	1.11.ab
\(13\)	\( 1 + 3 T + 13 T^{2}\)	1.13.d
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + T + 29 T^{2}\)	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 245.a do not have complex multiplication.

Modular form 245.2.a.a

Elliptic curves in class 245.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
245.a1	245a1	\([0, 0, 1, -7, 12]\)	\(-110592/125\)	\(-42875\)	\([]\)	\(48\)	\(-0.41676\)	\(\Gamma_0(N)\)-optimal