Elliptic curve isogeny class with Cremona label 165825a (LMFDB label 165825.a)

• Label: 165825a
• Number of curves: $1$
• Conductor: $165825$
• CM: no
• Rank: $1$

Rank

The elliptic curve 165825a1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1\)
\(11\)	\(1 + T\)
\(67\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T + 2 T^{2}\)	1.2.c
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 - 5 T + 29 T^{2}\)	1.29.af
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 165825a do not have complex multiplication.

Modular form 165825.2.a.a

Elliptic curves in class 165825a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
165825.a1	165825a1	\([0, 0, 1, 32875575, 1046428197156]\)	\(344981836779052322816/41728985197282986075\)	\(-475319222012801513260546875\)	\([]\)	\(122204160\)	\(3.7982\)	\(\Gamma_0(N)\)-optimal