Show commands:
SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 54096.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54096.s1 | 54096be1 | \([0, -1, 0, -237813, -44567235]\) | \(-62992384000/14283\) | \(-337259121389568\) | \([]\) | \(387072\) | \(1.7798\) | \(\Gamma_0(N)\)-optimal |
| 54096.s2 | 54096be2 | \([0, -1, 0, 91467, -155468739]\) | \(3584000000/444107667\) | \(-10486547754308677632\) | \([]\) | \(1161216\) | \(2.3291\) |
Rank
sage: E.rank()
The elliptic curves in class 54096.s have rank \(1\).
Complex multiplication
The elliptic curves in class 54096.s do not have complex multiplication.Modular form 54096.2.a.s
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
