Elliptic Curve Isogeny Class with LMFDB label 6270.l (Cremona label 6270l)

• Label: 6270.l
• Number of curves: 8
• Conductor: 6270
• CM: no
• Rank: 0

Elliptic curves in class 6270.l

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
6270.l1	6270l7	[1, 0, 1, -21424283, 37908785126]	[2]	774144
6270.l2	6270l4	[1, 0, 1, -21384008, 38059355306]	[6]	258048
6270.l3	6270l6	[1, 0, 1, -2257883, -324349594]	[2, 2]	387072
6270.l4	6270l3	[1, 0, 1, -1745883, -886935194]	[2]	193536
6270.l5	6270l2	[1, 0, 1, -1336508, 594587306]	[2, 6]	129024
6270.l6	6270l5	[1, 0, 1, -1289008, 638819306]	[6]	258048
6270.l7	6270l1	[1, 0, 1, -86508, 8587306]	[6]	64512	\(\Gamma_0(N)\)-optimal
6270.l8	6270l8	[1, 0, 1, 8716517, -2549957914]	[2]	774144

Rank

The elliptic curves in class 6270.l have rank \(0\).

Modular form 6270.2.a.l

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.