Elliptic curve isogeny class with LMFDB label 126126.cu (Cremona label 126126ca)

• Label: 126126.cu
• Number of curves: $1$
• Conductor: $126126$
• CM: no
• Rank: $1$

Rank

The elliptic curve 126126.cu1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1 + T\)
\(13\)	\(1 + T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 126126.cu do not have complex multiplication.

Modular form 126126.2.a.cu

Elliptic curves in class 126126.cu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
126126.cu1	126126ca1	\([1, -1, 0, -160533, -25818507]\)	\(-12808391413763617/674439727104\)	\(-24091661491881984\)	\([]\)	\(1115136\)	\(1.9027\)	\(\Gamma_0(N)\)-optimal