Elliptic curve isogeny class with Cremona label 9075l (LMFDB label 9075.g)

• Label: 9075l
• Number of curves: $8$
• Conductor: $9075$
• CM: no
• Rank: $1$

Elliptic curves in class 9075l

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9075.g7	9075l1	\([1, 0, 0, -63, -31008]\)	\(-1/15\)	\(-415209609375\)	\([2]\)	\(7680\)	\(0.90824\)	\(\Gamma_0(N)\)-optimal
9075.g6	9075l2	\([1, 0, 0, -15188, -711633]\)	\(13997521/225\)	\(6228144140625\)	\([2, 2]\)	\(15360\)	\(1.2548\)
9075.g4	9075l3	\([1, 0, 0, -242063, -45859758]\)	\(56667352321/15\)	\(415209609375\)	\([2]\)	\(30720\)	\(1.6014\)
9075.g5	9075l4	\([1, 0, 0, -30313, 936992]\)	\(111284641/50625\)	\(1401332431640625\)	\([2, 2]\)	\(30720\)	\(1.6014\)
9075.g2	9075l5	\([1, 0, 0, -408438, 100383867]\)	\(272223782641/164025\)	\(4540317078515625\)	\([2, 2]\)	\(61440\)	\(1.9480\)
9075.g8	9075l6	\([1, 0, 0, 105812, 7062617]\)	\(4733169839/3515625\)	\(-97314752197265625\)	\([2]\)	\(61440\)	\(1.9480\)
9075.g1	9075l7	\([1, 0, 0, -6534063, 6428154492]\)	\(1114544804970241/405\)	\(11210659453125\)	\([2]\)	\(122880\)	\(2.2945\)
9075.g3	9075l8	\([1, 0, 0, -332813, 138725742]\)	\(-147281603041/215233605\)	\(-5957804070428203125\)	\([2]\)	\(122880\)	\(2.2945\)

Rank

The elliptic curves in class 9075l have rank \(1\).

Complex multiplication

The elliptic curves in class 9075l do not have complex multiplication.

Modular form 9075.2.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 Cremona numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 8 & 8 & 16 & 16 \\ 4 & 2 & 4 & 1 & 2 & 2 & 4 & 4 \\ 8 & 4 & 8 & 2 & 1 & 4 & 2 & 2 \\ 8 & 4 & 8 & 2 & 4 & 1 & 8 & 8 \\ 16 & 8 & 16 & 4 & 2 & 8 & 1 & 4 \\ 16 & 8 & 16 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.