Elliptic curve isogeny class with Cremona label 257600ff (LMFDB label 257600.ff)

• Label: 257600ff
• Number of curves: $2$
• Conductor: $257600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 257600ff have rank \(0\).

L-function data

Bad L-factors:

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

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.e
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 257600ff do not have complex multiplication.

Modular form 257600.2.a.ff

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 257600ff

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
257600.ff1	257600ff1	\([0, -1, 0, -4033, -12063]\)	\(7086244/4025\)	\(4121600000000\)	\([2]\)	\(393216\)	\(1.1105\)	\(\Gamma_0(N)\)-optimal
257600.ff2	257600ff2	\([0, -1, 0, 15967, -112063]\)	\(219804478/129605\)	\(-265431040000000\)	\([2]\)	\(786432\)	\(1.4571\)