Show commands:
SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 107712.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 107712.s1 | 107712cn2 | \([0, 0, 0, -706476, 131985200]\) | \(204055591784617/78708537864\) | \(15041435822419083264\) | \([2]\) | \(2064384\) | \(2.3788\) | |
| 107712.s2 | 107712cn1 | \([0, 0, 0, -314796, -66518224]\) | \(18052771191337/444958272\) | \(85032849975017472\) | \([2]\) | \(1032192\) | \(2.0322\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 107712.s have rank \(0\).
Complex multiplication
The elliptic curves in class 107712.s do not have complex multiplication.Modular form 107712.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
