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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 2496o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2496.r2 | 2496o1 | \([0, 1, 0, -624, 9486]\) | \(-420526439488/390971529\) | \(-25022177856\) | \([2]\) | \(1536\) | \(0.69180\) | \(\Gamma_0(N)\)-optimal |
| 2496.r1 | 2496o2 | \([0, 1, 0, -11609, 477447]\) | \(42246001231552/14414517\) | \(59041861632\) | \([2]\) | \(3072\) | \(1.0384\) |
Rank
sage: E.rank()
The elliptic curves in class 2496o have rank \(1\).
Complex multiplication
The elliptic curves in class 2496o do not have complex multiplication.Modular form 2496.2.a.o
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.
