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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 40656o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40656.bl2 | 40656o1 | \([0, -1, 0, 5768, 296320]\) | \(8788/21\) | \(-50705307147264\) | \([2]\) | \(84480\) | \(1.3137\) | \(\Gamma_0(N)\)-optimal |
| 40656.bl1 | 40656o2 | \([0, -1, 0, -47472, 3320352]\) | \(2450086/441\) | \(2129622900185088\) | \([2]\) | \(168960\) | \(1.6603\) |
Rank
sage: E.rank()
The elliptic curves in class 40656o have rank \(0\).
Complex multiplication
The elliptic curves in class 40656o do not have complex multiplication.Modular form 40656.2.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.
