Elliptic curve isogeny class with LMFDB label 41574.g (Cremona label 41574j)

• Label: 41574.g
• Number of curves: $1$
• Conductor: $41574$
• CM: no
• Rank: $2$

Rank

The elliptic curve 41574.g1 has rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 - T\)
\(13\)	\(1\)
\(41\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 41574.g do not have complex multiplication.

Modular form 41574.2.a.g

Elliptic curves in class 41574.g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
41574.g1	41574j1	\([1, 0, 1, -485, -700]\)	\(5725732069/3228012\)	\(7091942364\)	\([]\)	\(55296\)	\(0.58025\)	\(\Gamma_0(N)\)-optimal