Elliptic curve isogeny class with LMFDB label 41405.n (Cremona label 41405a)

• Label: 41405.n
• Number of curves: $1$
• Conductor: $41405$
• CM: no
• Rank: $1$

Rank

The elliptic curve 41405.n1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 41405.n do not have complex multiplication.

Modular form 41405.2.a.n

Isogeny graph

Elliptic curves in class 41405.n

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
41405.n1	41405a1	\([1, 1, 0, -8453, -4588618]\)	\(-2401/325\)	\(-9043317838752925\)	\([]\)	\(282240\)	\(1.7412\)	\(\Gamma_0(N)\)-optimal