Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 53361.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 53361.h1 | 53361ca3 | \([0, 0, 1, -417300807, 3281118763788]\) | \(-52893159101157376/11\) | \(-1671339065933691\) | \([]\) | \(6480000\) | \(3.2179\) | |
| 53361.h2 | 53361ca2 | \([0, 0, 1, -551397, 285447258]\) | \(-122023936/161051\) | \(-24470075264335169931\) | \([]\) | \(1296000\) | \(2.4132\) | |
| 53361.h3 | 53361ca1 | \([0, 0, 1, -17787, -2168532]\) | \(-4096/11\) | \(-1671339065933691\) | \([]\) | \(259200\) | \(1.6085\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 53361.h have rank \(0\).
Complex multiplication
The elliptic curves in class 53361.h do not have complex multiplication.Modular form 53361.2.a.h
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().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.
\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
