Elliptic curve isogeny class with Cremona label 213444b (LMFDB label 213444.e)

• Label: 213444b
• Number of curves: $1$
• Conductor: $213444$
• CM: no
• Rank: $1$

Rank

The elliptic curve 213444b1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 7 T + 17 T^{2}\)	1.17.ah
\(19\)	\( 1 + 3 T + 19 T^{2}\)	1.19.d
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 213444b do not have complex multiplication.

Modular form 213444.2.a.b

Elliptic curves in class 213444b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
213444.e1	213444b1	\([0, 0, 0, -10956792, 13960779140]\)	\(-30908416/3\)	\(-14119472429007821568\)	\([]\)	\(10378368\)	\(2.7103\)	\(\Gamma_0(N)\)-optimal