Elliptic curve isogeny class with LMFDB label 2057.e (Cremona label 2057c)

• Label: 2057.e
• Number of curves: $4$
• Conductor: $2057$
• CM: no
• Rank: $0$

Elliptic curves in class 2057.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2057.e1	2057c3	\([1, -1, 0, -10973, 445176]\)	\(82483294977/17\)	\(30116537\)	\([2]\)	\(1440\)	\(0.82231\)
2057.e2	2057c2	\([1, -1, 0, -688, 7035]\)	\(20346417/289\)	\(511981129\)	\([2, 2]\)	\(720\)	\(0.47574\)
2057.e3	2057c1	\([1, -1, 0, -83, -104]\)	\(35937/17\)	\(30116537\)	\([2]\)	\(360\)	\(0.12916\)	\(\Gamma_0(N)\)-optimal
2057.e4	2057c4	\([1, -1, 0, -83, 18530]\)	\(-35937/83521\)	\(-147962546281\)	\([2]\)	\(1440\)	\(0.82231\)

Rank

The elliptic curves in class 2057.e have rank \(0\).

Complex multiplication

The elliptic curves in class 2057.e do not have complex multiplication.

Modular form 2057.2.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 LMFDB 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 LMFDB labels.