Elliptic curve isogeny class with LMFDB label 17424.z (Cremona label 17424p)

• Label: 17424.z
• Number of curves: $1$
• Conductor: $17424$
• CM: no
• Rank: $1$

Rank

The elliptic curve 17424.z1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 17424.z do not have complex multiplication.

Modular form 17424.2.a.z

Elliptic curves in class 17424.z

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17424.z1	17424p1	\([0, 0, 0, -660, 7436]\)	\(-1408000/243\)	\(-5487305472\)	\([]\)	\(7680\)	\(0.59501\)	\(\Gamma_0(N)\)-optimal