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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 209484c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 209484.c2 | 209484c1 | \([0, 0, 0, -787152, -111997235]\) | \(31238127616/14939397\) | \(25795716508444834512\) | \([2]\) | \(6082560\) | \(2.4186\) | \(\Gamma_0(N)\)-optimal |
| 209484.c1 | 209484c2 | \([0, 0, 0, -6571767, 6407263870]\) | \(1136150003536/15554187\) | \(429716298050142757632\) | \([2]\) | \(12165120\) | \(2.7652\) |
Rank
sage: E.rank()
The elliptic curves in class 209484c have rank \(1\).
Complex multiplication
The elliptic curves in class 209484c do not have complex multiplication.Modular form 209484.2.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.
