Elliptic curve isogeny class with LMFDB label 4335.c (Cremona label 4335d)

• Label: 4335.c
• Number of curves: $8$
• Conductor: $4335$
• CM: no
• Rank: $0$

Elliptic curves in class 4335.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4335.c1	4335d7	\([1, 0, 0, -624246, -189889425]\)	\(1114544804970241/405\)	\(9775715445\)	\([2]\)	\(20480\)	\(1.7075\)
4335.c2	4335d5	\([1, 0, 0, -39021, -2968560]\)	\(272223782641/164025\)	\(3959164755225\)	\([2, 2]\)	\(10240\)	\(1.3609\)
4335.c3	4335d8	\([1, 0, 0, -31796, -4099995]\)	\(-147281603041/215233605\)	\(-5195215991806245\)	\([2]\)	\(20480\)	\(1.7075\)
4335.c4	4335d4	\([1, 0, 0, -23126, 1351701]\)	\(56667352321/15\)	\(362063535\)	\([2]\)	\(5120\)	\(1.0143\)
4335.c5	4335d3	\([1, 0, 0, -2896, -27985]\)	\(111284641/50625\)	\(1221964430625\)	\([2, 2]\)	\(5120\)	\(1.0143\)
4335.c6	4335d2	\([1, 0, 0, -1451, 20856]\)	\(13997521/225\)	\(5430953025\)	\([2, 2]\)	\(2560\)	\(0.66776\)
4335.c7	4335d1	\([1, 0, 0, -6, 915]\)	\(-1/15\)	\(-362063535\)	\([2]\)	\(1280\)	\(0.32118\)	\(\Gamma_0(N)\)-optimal
4335.c8	4335d6	\([1, 0, 0, 10109, -207454]\)	\(4733169839/3515625\)	\(-84858641015625\)	\([2]\)	\(10240\)	\(1.3609\)

Rank

The elliptic curves in class 4335.c have rank \(0\).

Complex multiplication

The elliptic curves in class 4335.c do not have complex multiplication.

Modular form 4335.2.a.c

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.