Elliptic curve isogeny class with Cremona label 176400ql (LMFDB label 176400.rs)

• Label: 176400ql
• Number of curves: $4$
• Conductor: $176400$
• CM: no
• Rank: $1$

Elliptic curves in class 176400ql

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
176400.rs3	176400ql1	\([0, 0, 0, -3487575, 2506729750]\)	\(13674725584/945\)	\(324195937380000000\)	\([2]\)	\(3538944\)	\(2.4137\)	\(\Gamma_0(N)\)-optimal
176400.rs2	176400ql2	\([0, 0, 0, -3708075, 2171790250]\)	\(4108974916/893025\)	\(1225460643296400000000\)	\([2, 2]\)	\(7077888\)	\(2.7603\)
176400.rs4	176400ql3	\([0, 0, 0, 8198925, 13257207250]\)	\(22208984782/40516875\)	\(-111199206521340000000000\)	\([2]\)	\(14155776\)	\(3.1069\)
176400.rs1	176400ql4	\([0, 0, 0, -19143075, -30349754750]\)	\(282678688658/18600435\)	\(51049189083604320000000\)	\([2]\)	\(14155776\)	\(3.1069\)

Rank

The elliptic curves in class 176400ql have rank \(1\).

Complex multiplication

The elliptic curves in class 176400ql do not have complex multiplication.

Modular form 176400.2.a.ql

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.