Elliptic curve isogeny class with Cremona label 17918e (LMFDB label 17918.e)

• Label: 17918e
• Number of curves: $4$
• Conductor: $17918$
• CM: no
• Rank: $1$

Elliptic curves in class 17918e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17918.e4	17918e1	\([1, -1, 1, -199, 5423]\)	\(-35937/496\)	\(-11972234224\)	\([2]\)	\(9216\)	\(0.61538\)	\(\Gamma_0(N)\)-optimal
17918.e3	17918e2	\([1, -1, 1, -5979, 178823]\)	\(979146657/3844\)	\(92784815236\)	\([2, 2]\)	\(18432\)	\(0.96196\)
17918.e2	17918e3	\([1, -1, 1, -8869, -9605]\)	\(3196010817/1847042\)	\(44583103720898\)	\([2]\)	\(36864\)	\(1.3085\)
17918.e1	17918e4	\([1, -1, 1, -95569, 11395491]\)	\(3999236143617/62\)	\(1496529278\)	\([2]\)	\(36864\)	\(1.3085\)

Rank

The elliptic curves in class 17918e have rank \(1\).

Complex multiplication

The elliptic curves in class 17918e do not have complex multiplication.

Modular form 17918.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.