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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 705600.c
sage: E.isogeny_class().curves
| LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
|---|---|---|---|---|---|---|
| 705600.c1 | \([0, 0, 0, -244020, 46373600]\) | \(36594368/21\) | \(922157332992000\) | \([2]\) | \(6291456\) | \(1.8175\) |
| 705600.c2 | \([0, 0, 0, -12495, 994700]\) | \(-314432/441\) | \(-302582874888000\) | \([2]\) | \(3145728\) | \(1.4709\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.c have rank \(2\).
Complex multiplication
The elliptic curves in class 705600.c do not have complex multiplication.Modular form 705600.2.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 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.
