Elliptic curve isogeny class with Cremona label 344850eq (LMFDB label 344850.eq)

• Label: 344850eq
• Number of curves: $4$
• Conductor: $344850$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 344850eq have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(11\)	\(1\)
\(19\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 344850eq do not have complex multiplication.

Modular form 344850.2.a.eq

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 344850eq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
344850.eq4	344850eq1	\([1, 1, 1, 28238312, 122823288281]\)	\(89962967236397039/287450726400000\)	\(-7956820254873600000000000\)	\([2]\)	\(80640000\)	\(3.4612\)	\(\Gamma_0(N)\)-optimal
344850.eq3	344850eq2	\([1, 1, 1, -266033688, 1438807672281]\)	\(75224183150104868881/11219310000000000\)	\(310557688170468750000000000\)	\([2]\)	\(161280000\)	\(3.8078\)
344850.eq2	344850eq3	\([1, 1, 1, -9986931688, 384141888168281]\)	\(-3979640234041473454886161/1471455901872240\)	\(-40730842015260740103750000\)	\([2]\)	\(403200000\)	\(4.2659\)
344850.eq1	344850eq4	\([1, 1, 1, -159790921188, 24585275999872281]\)	\(16300610738133468173382620881/2228489100\)	\(61686005913829687500\)	\([2]\)	\(806400000\)	\(4.6125\)