Elliptic curve isogeny class with LMFDB label 65025.k (Cremona label 65025cl)

• Label: 65025.k
• Number of curves: $1$
• Conductor: $65025$
• CM: no
• Rank: $0$

Rank

The elliptic curve 65025.k1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + T + 2 T^{2}\)	1.2.b
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 65025.k do not have complex multiplication.

Modular form 65025.2.a.k

Elliptic curves in class 65025.k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
65025.k1	65025cl1	\([1, -1, 1, -196430, -6210678]\)	\(35242105/19683\)	\(468138695916796875\)	\([]\)	\(544320\)	\(2.0809\)	\(\Gamma_0(N)\)-optimal