Elliptic curve isogeny class with LMFDB label 726.f (Cremona label 726g)

• Label: 726.f
• Number of curves: $1$
• Conductor: $726$
• CM: no
• Rank: $1$

Rank

The elliptic curve 726.f1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 + T\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(17\)	\( 1 + T + 17 T^{2}\)	1.17.b
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 726.f do not have complex multiplication.

Modular form 726.2.a.f

Elliptic curves in class 726.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
726.f1	726g1	\([1, 1, 1, 179, 1475]\)	\(43307231/82944\)	\(-1214383104\)	\([]\)	\(480\)	\(0.42772\)	\(\Gamma_0(N)\)-optimal