Elliptic curve isogeny class with LMFDB label 333564.e (Cremona label 333564e)

• Label: 333564.e
• Number of curves: $1$
• Conductor: $333564$
• CM: no
• Rank: $0$

Rank

The elliptic curve 333564.e1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(7\)	\(1 + T\)
\(11\)	\(1 - T\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 7 T + 29 T^{2}\)	1.29.h
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 333564.e do not have complex multiplication.

Modular form 333564.2.a.e

Elliptic curves in class 333564.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
333564.e1	333564e1	\([0, -1, 0, -615986, 186291777]\)	\(-34339609640704/916839\)	\(-690135975842544\)	\([]\)	\(2533680\)	\(1.9523\)	\(\Gamma_0(N)\)-optimal