Elliptic curve isogeny class with Cremona label 285318c (LMFDB label 285318.c)

• Label: 285318c
• Number of curves: $4$
• Conductor: $285318$
• CM: no
• Rank: $2$

Elliptic curves in class 285318c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
285318.c4	285318c1	\([1, -1, 0, -32148, 339664]\)	\(2845178713/1609728\)	\(2078912150802432\)	\([2]\)	\(1474560\)	\(1.6292\)	\(\Gamma_0(N)\)-optimal
285318.c2	285318c2	\([1, -1, 0, -380628, 90317200]\)	\(4722184089433/9884736\)	\(12765819926021184\)	\([2, 2]\)	\(2949120\)	\(1.9758\)
285318.c1	285318c3	\([1, -1, 0, -6086988, 5781840664]\)	\(19312898130234073/84888\)	\(109630132952472\)	\([2]\)	\(5898240\)	\(2.3223\)
285318.c3	285318c4	\([1, -1, 0, -249948, 153174280]\)	\(-1337180541913/7067998104\)	\(-9128093156268730776\)	\([2]\)	\(5898240\)	\(2.3223\)

Rank

The elliptic curves in class 285318c have rank \(2\).

Complex multiplication

The elliptic curves in class 285318c do not have complex multiplication.

Modular form 285318.2.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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.