Elliptic curve isogeny class with Cremona label 37485u (LMFDB label 37485.l)

• Label: 37485u
• Number of curves: $4$
• Conductor: $37485$
• CM: no
• Rank: $1$

Elliptic curves in class 37485u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
37485.l4	37485u1	\([1, -1, 1, 126337, 2407542]\)	\(2600176603751/1534698375\)	\(-131625126528753375\)	\([2]\)	\(294912\)	\(1.9743\)	\(\Gamma_0(N)\)-optimal
37485.l3	37485u2	\([1, -1, 1, -510908, 19740606]\)	\(171963096231529/97578140625\)	\(8368898615798765625\)	\([2, 2]\)	\(589824\)	\(2.3208\)
37485.l2	37485u3	\([1, -1, 1, -5196533, -4536561144]\)	\(180945977944161529/992266372125\)	\(85102837735903777125\)	\([2]\)	\(1179648\)	\(2.6674\)
37485.l1	37485u4	\([1, -1, 1, -6021203, 5677711512]\)	\(281486573281608409/610107421875\)	\(52326546967529296875\)	\([2]\)	\(1179648\)	\(2.6674\)

Rank

The elliptic curves in class 37485u have rank \(1\).

Complex multiplication

The elliptic curves in class 37485u do not have complex multiplication.

Modular form 37485.2.a.u

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.