Elliptic curve isogeny class with Cremona label 259350gr (LMFDB label 259350.gr)

• Label: 259350gr
• Number of curves: $4$
• Conductor: $259350$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 259350gr have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(13\)	\(1 + T\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 259350gr do not have complex multiplication.

Modular form 259350.2.a.gr

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 259350gr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
259350.gr4	259350gr1	\([1, 0, 0, -355338, -85599708]\)	\(-317562142497484249/18670942617600\)	\(-291733478400000000\)	\([2]\)	\(3932160\)	\(2.1071\)	\(\Gamma_0(N)\)-optimal
259350.gr3	259350gr2	\([1, 0, 0, -5763338, -5325951708]\)	\(1354958399265695661529/4304795040000\)	\(67262422500000000\)	\([2, 2]\)	\(7864320\)	\(2.4537\)
259350.gr2	259350gr3	\([1, 0, 0, -5841338, -5174397708]\)	\(1410719602237262088409/76269550743750000\)	\(1191711730371093750000\)	\([2]\)	\(15728640\)	\(2.8003\)
259350.gr1	259350gr4	\([1, 0, 0, -92213338, -340838401708]\)	\(5549896908024170183373529/56019600\)	\(875306250000\)	\([2]\)	\(15728640\)	\(2.8003\)