Elliptic curve isogeny class with LMFDB label 2574.t (Cremona label 2574t)

• Label: 2574.t
• Number of curves: $4$
• Conductor: $2574$
• CM: no
• Rank: $1$

Elliptic curves in class 2574.t

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2574.t1	2574t4	\([1, -1, 1, -44951, 3679431]\)	\(13778603383488553/13703976\)	\(9990198504\)	\([2]\)	\(6144\)	\(1.2114\)
2574.t2	2574t3	\([1, -1, 1, -6791, -134553]\)	\(47504791830313/16490207448\)	\(12021361229592\)	\([2]\)	\(6144\)	\(1.2114\)
2574.t3	2574t2	\([1, -1, 1, -2831, 57111]\)	\(3440899317673/106007616\)	\(77279552064\)	\([2, 2]\)	\(3072\)	\(0.86486\)
2574.t4	2574t1	\([1, -1, 1, 49, 2967]\)	\(18191447/5271552\)	\(-3842961408\)	\([2]\)	\(1536\)	\(0.51829\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 2574.t have rank \(1\).

Complex multiplication

The elliptic curves in class 2574.t do not have complex multiplication.

Modular form 2574.2.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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.