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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 57222c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57222.p1 | 57222c1 | \([1, -1, 0, -944217, 348411613]\) | \(1076890625/17424\) | \(1506314591701037712\) | \([2]\) | \(835584\) | \(2.2876\) | \(\Gamma_0(N)\)-optimal |
| 57222.p2 | 57222c2 | \([1, -1, 0, -59877, 974347465]\) | \(-274625/4743684\) | \(-410094147590607517092\) | \([2]\) | \(1671168\) | \(2.6341\) |
Rank
sage: E.rank()
The elliptic curves in class 57222c have rank \(0\).
Complex multiplication
The elliptic curves in class 57222c do not have complex multiplication.Modular form 57222.2.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.
