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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 259920b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 259920.b2 | 259920b1 | \([0, 0, 0, 15162, -294937]\) | \(702464/475\) | \(-260652999092400\) | \([2]\) | \(1105920\) | \(1.4549\) | \(\Gamma_0(N)\)-optimal |
| 259920.b1 | 259920b2 | \([0, 0, 0, -66063, -2455522]\) | \(3631696/1805\) | \(15847702344817920\) | \([2]\) | \(2211840\) | \(1.8014\) |
Rank
sage: E.rank()
The elliptic curves in class 259920b have rank \(1\).
Complex multiplication
The elliptic curves in class 259920b do not have complex multiplication.Modular form 259920.2.a.b
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.
