Elliptic curve isogeny class with Cremona label 735e (LMFDB label 735.c)

• Label: 735e
• Number of curves: $8$
• Conductor: $735$
• CM: no
• Rank: $1$

Elliptic curves in class 735e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
735.c7	735e1	\([1, 0, 0, -1, -64]\)	\(-1/15\)	\(-1764735\)	\([2]\)	\(96\)	\(-0.12247\)	\(\Gamma_0(N)\)-optimal
735.c6	735e2	\([1, 0, 0, -246, -1485]\)	\(13997521/225\)	\(26471025\)	\([2, 2]\)	\(192\)	\(0.22410\)
735.c4	735e3	\([1, 0, 0, -3921, -94830]\)	\(56667352321/15\)	\(1764735\)	\([2]\)	\(384\)	\(0.57068\)
735.c5	735e4	\([1, 0, 0, -491, 1896]\)	\(111284641/50625\)	\(5955980625\)	\([2, 2]\)	\(384\)	\(0.57068\)
735.c2	735e5	\([1, 0, 0, -6616, 206471]\)	\(272223782641/164025\)	\(19297377225\)	\([2, 2]\)	\(768\)	\(0.91725\)
735.c8	735e6	\([1, 0, 0, 1714, 14685]\)	\(4733169839/3515625\)	\(-413609765625\)	\([2]\)	\(768\)	\(0.91725\)
735.c1	735e7	\([1, 0, 0, -105841, 13244636]\)	\(1114544804970241/405\)	\(47647845\)	\([2]\)	\(1536\)	\(1.2638\)
735.c3	735e8	\([1, 0, 0, -5391, 285606]\)	\(-147281603041/215233605\)	\(-25322018394645\)	\([2]\)	\(1536\)	\(1.2638\)

Rank

The elliptic curves in class 735e have rank \(1\).

Complex multiplication

The elliptic curves in class 735e do not have complex multiplication.

Modular form 735.2.a.e

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.