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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 235200c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235200.c1 | 235200c1 | \([0, -1, 0, -1709633, -490108863]\) | \(393349474783/153600000\) | \(215796940800000000000\) | \([2]\) | \(10321920\) | \(2.6005\) | \(\Gamma_0(N)\)-optimal |
| 235200.c2 | 235200c2 | \([0, -1, 0, 5458367, -3536508863]\) | \(12801408679457/11250000000\) | \(-15805440000000000000000\) | \([2]\) | \(20643840\) | \(2.9470\) |
Rank
sage: E.rank()
The elliptic curves in class 235200c have rank \(0\).
Complex multiplication
The elliptic curves in class 235200c do not have complex multiplication.Modular form 235200.2.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.
