Elliptic curve isogeny class with Cremona label 37485r (LMFDB label 37485.bc)

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

Elliptic curves in class 37485r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
37485.bc4	37485r1	\([1, -1, 0, -79830, -19709649]\)	\(-656008386769/1581036975\)	\(-135599408503323975\)	\([2]\)	\(294912\)	\(1.9755\)	\(\Gamma_0(N)\)-optimal
37485.bc3	37485r2	\([1, -1, 0, -1687275, -842400000]\)	\(6193921595708449/6452105625\)	\(553372071738530625\)	\([2, 2]\)	\(589824\)	\(2.3221\)
37485.bc2	37485r3	\([1, -1, 0, -2104020, -394065729]\)	\(12010404962647729/6166198828125\)	\(528850954803026953125\)	\([2]\)	\(1179648\)	\(2.6686\)
37485.bc1	37485r4	\([1, -1, 0, -26989650, -53962206075]\)	\(25351269426118370449/27551475\)	\(2362983138578475\)	\([2]\)	\(1179648\)	\(2.6686\)

Rank

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

Complex multiplication

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

Modular form 37485.2.a.r

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.