Elliptic curve isogeny class with Cremona label 61a (LMFDB label 61.a)

• Label: 61a
• Number of curves: $1$
• Conductor: $61$
• CM: no
• Rank: $1$

Rank

The elliptic curve 61a1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(61\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + T + 2 T^{2}\)	1.2.b
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 9 T + 23 T^{2}\)	1.23.j
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 61a do not have complex multiplication.

Modular form 61.2.a.a

Elliptic curves in class 61a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
61.a1	61a1	\([1, 0, 0, -2, 1]\)	\(-912673/61\)	\(-61\)	\([]\)	\(2\)	\(-0.90546\)	\(\Gamma_0(N)\)-optimal