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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 260710c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 260710.c2 | 260710c1 | \([1, 0, 1, -55524, -5207134]\) | \(-31824875809/1240000\) | \(-737580918040000\) | \([2]\) | \(1188096\) | \(1.6220\) | \(\Gamma_0(N)\)-optimal |
| 260710.c1 | 260710c2 | \([1, 0, 1, -896524, -326805534]\) | \(133974081659809/192200\) | \(114325042296200\) | \([2]\) | \(2376192\) | \(1.9686\) |
Rank
sage: E.rank()
The elliptic curves in class 260710c have rank \(0\).
Complex multiplication
The elliptic curves in class 260710c do not have complex multiplication.Modular form 260710.2.a.c
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 Cremona 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 Cremona labels.
