Elliptic curve isogeny class with LMFDB label 57498.t (Cremona label 57498r)

• Label: 57498.t
• Number of curves: $4$
• Conductor: $57498$
• CM: no
• Rank: $1$

Elliptic curves in class 57498.t

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
57498.t1	57498r4	\([1, 0, 0, -30256982, 64057418100]\)	\(1193961132635558617/335664\)	\(861221989350576\)	\([2]\)	\(2101248\)	\(2.6733\)
57498.t2	57498r2	\([1, 0, 0, -1891302, 1000511460]\)	\(291605712526297/154554624\)	\(396544880429865216\)	\([2, 2]\)	\(1050624\)	\(2.3267\)
57498.t3	57498r3	\([1, 0, 0, -1562742, 1359364692]\)	\(-164503536215257/215993306928\)	\(-554179731752412261552\)	\([2]\)	\(2101248\)	\(2.6733\)
57498.t4	57498r1	\([1, 0, 0, -138982, 9749732]\)	\(115714886617/50921472\)	\(130650565495554048\)	\([2]\)	\(525312\)	\(1.9801\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 57498.t have rank \(1\).

Complex multiplication

The elliptic curves in class 57498.t do not have complex multiplication.

Modular form 57498.2.a.t

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.