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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 7650o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7650.z1 | 7650o1 | \([1, -1, 0, -567, -3159]\) | \(1771561/612\) | \(6971062500\) | \([2]\) | \(5120\) | \(0.59050\) | \(\Gamma_0(N)\)-optimal |
| 7650.z2 | 7650o2 | \([1, -1, 0, 1683, -23409]\) | \(46268279/46818\) | \(-533286281250\) | \([2]\) | \(10240\) | \(0.93707\) |
Rank
sage: E.rank()
The elliptic curves in class 7650o have rank \(0\).
Complex multiplication
The elliptic curves in class 7650o do not have complex multiplication.Modular form 7650.2.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.
