Elliptic curve isogeny class with LMFDB label 34496.f (Cremona label 34496bv)

• Label: 34496.f
• Number of curves: $1$
• Conductor: $34496$
• CM: no
• Rank: $1$

Rank

The elliptic curve 34496.f1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T + 3 T^{2}\)	1.3.d
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - T + 29 T^{2}\)	1.29.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 34496.f do not have complex multiplication.

Modular form 34496.2.a.f

Elliptic curves in class 34496.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
34496.f1	34496bv1	\([0, 0, 0, -83020, 9203152]\)	\(39411764973000/19487171\)	\(31289225347072\)	\([]\)	\(172032\)	\(1.5428\)	\(\Gamma_0(N)\)-optimal