Elliptic curve isogeny class with Cremona label 26714i (LMFDB label 26714.c)

• Label: 26714i
• Number of curves: $1$
• Conductor: $26714$
• CM: no
• Rank: $1$

Rank

The elliptic curve 26714i1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(19\)	\(1\)
\(37\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 26714i do not have complex multiplication.

Modular form 26714.2.a.i

Elliptic curves in class 26714i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
26714.c1	26714i1	\([1, 1, 0, -6866, 637876]\)	\(-761048497/3329408\)	\(-156634932568448\)	\([]\)	\(80640\)	\(1.4087\)	\(\Gamma_0(N)\)-optimal