Elliptic curve isogeny class with LMFDB label 35574.a (Cremona label 35574o)

• Label: 35574.a
• Number of curves: $4$
• Conductor: $35574$
• CM: no
• Rank: $1$

Elliptic curves in class 35574.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
35574.a1	35574o4	\([1, 1, 0, -238624586, 1418699640450]\)	\(7209828390823479793/49509306\)	\(10318847393074608234\)	\([2]\)	\(4423680\)	\(3.2481\)
35574.a2	35574o3	\([1, 1, 0, -20793126, 3095418726]\)	\(4770223741048753/2740574865798\)	\(571197136341710922296022\)	\([2]\)	\(4423680\)	\(3.2481\)
35574.a3	35574o2	\([1, 1, 0, -14923416, 22133236140]\)	\(1763535241378513/4612311396\)	\(961308918865938194244\)	\([2, 2]\)	\(2211840\)	\(2.9016\)
35574.a4	35574o1	\([1, 1, 0, -575236, 613835776]\)	\(-100999381393/723148272\)	\(-150720284007487556208\)	\([2]\)	\(1105920\)	\(2.5550\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 35574.a have rank \(1\).

Complex multiplication

The elliptic curves in class 35574.a do not have complex multiplication.

Modular form 35574.2.a.a

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.