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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 244881s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 244881.s2 | 244881s1 | \([1, -1, 1, 25825, 1589046]\) | \(541343375/625807\) | \(-2202054476840127\) | \([2]\) | \(967680\) | \(1.6304\) | \(\Gamma_0(N)\)-optimal |
| 244881.s1 | 244881s2 | \([1, -1, 1, -149090, 15162450]\) | \(104154702625/32188247\) | \(113262193308776967\) | \([2]\) | \(1935360\) | \(1.9769\) |
Rank
sage: E.rank()
The elliptic curves in class 244881s have rank \(1\).
Complex multiplication
The elliptic curves in class 244881s do not have complex multiplication.Modular form 244881.2.a.s
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.
