Elliptic curve isogeny class with Cremona label 360640ig (LMFDB label 360640.ig)

• Label: 360640ig
• Number of curves: $2$
• Conductor: $360640$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 360640ig have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 - T\)
\(7\)	\(1\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 360640ig do not have complex multiplication.

Modular form 360640.2.a.ig

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 360640ig

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
360640.ig1	360640ig1	\([0, -1, 0, -7905, 39425]\)	\(7086244/4025\)	\(31033735577600\)	\([2]\)	\(786432\)	\(1.2787\)	\(\Gamma_0(N)\)-optimal
360640.ig2	360640ig2	\([0, -1, 0, 31295, 282465]\)	\(219804478/129605\)	\(-1998572571197440\)	\([2]\)	\(1572864\)	\(1.6253\)