Elliptic curve isogeny class with LMFDB label 253575.fd (Cremona label 253575fd)

• Label: 253575.fd
• Number of curves: $4$
• Conductor: $253575$
• CM: no
• Rank: $0$

Elliptic curves in class 253575.fd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
253575.fd1	253575fd3	\([1, -1, 0, -47336067, 125365306716]\)	\(8753151307882969/65205\)	\(87380936246953125\)	\([2]\)	\(12976128\)	\(2.8453\)
253575.fd2	253575fd2	\([1, -1, 0, -2960442, 1956693591]\)	\(2141202151369/5832225\)	\(7815739297644140625\)	\([2, 2]\)	\(6488064\)	\(2.4987\)
253575.fd3	253575fd4	\([1, -1, 0, -1802817, 3502122966]\)	\(-483551781049/3672913125\)	\(-4922054867206845703125\)	\([2]\)	\(12976128\)	\(2.8453\)
253575.fd4	253575fd1	\([1, -1, 0, -259317, 3780216]\)	\(1439069689/828345\)	\(1110061523433515625\)	\([2]\)	\(3244032\)	\(2.1522\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 253575.fd have rank \(0\).

Complex multiplication

The elliptic curves in class 253575.fd do not have complex multiplication.

Modular form 253575.2.a.fd

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.