Elliptic curve isogeny class with Cremona label 258720de (LMFDB label 258720.de)

• Label: 258720de
• Number of curves: $4$
• Conductor: $258720$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 258720de have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(11\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 258720de do not have complex multiplication.

Modular form 258720.2.a.de

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 258720de

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
258720.de3	258720de1	\([0, 1, 0, -393486, 57563064]\)	\(894838079076544/326869475625\)	\(2461175484019560000\)	\([2, 2]\)	\(3538944\)	\(2.2293\)	\(\Gamma_0(N)\)-optimal
258720.de1	258720de2	\([0, 1, 0, -5581361, 5072163039]\)	\(39902117402149696/11253263175\)	\(5422838412392755200\)	\([4]\)	\(7077888\)	\(2.5759\)
258720.de4	258720de3	\([0, 1, 0, 1207344, 408465000]\)	\(3231158304084472/3064088671875\)	\(-184569327696600000000\)	\([2]\)	\(7077888\)	\(2.5759\)
258720.de2	258720de4	\([0, 1, 0, -2708736, -1675170036]\)	\(36489314991346568/1012845712725\)	\(61010066051268364800\)	\([2]\)	\(7077888\)	\(2.5759\)