Elliptic curve isogeny class with LMFDB label 45968.x (Cremona label 45968n)

• Label: 45968.x
• Number of curves: $1$
• Conductor: $45968$
• CM: no
• Rank: $0$

Rank

The elliptic curve 45968.x1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(13\)	\(1\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 3 T + 3 T^{2}\)	1.3.ad
\(5\)	\( 1 - 4 T + 5 T^{2}\)	1.5.ae
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 45968.x do not have complex multiplication.

Modular form 45968.2.a.x

Elliptic curves in class 45968.x

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
45968.x1	45968n1	\([0, 0, 0, -11510083, 15033653570]\)	\(-298652123601/78608\)	\(-44387452220482322432\)	\([]\)	\(5211648\)	\(2.7545\)	\(\Gamma_0(N)\)-optimal