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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 355740s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 355740.s2 | 355740s1 | \([0, -1, 0, 86959, 47027730]\) | \(16384/225\) | \(-998676676434452400\) | \([2]\) | \(4561920\) | \(2.1345\) | \(\Gamma_0(N)\)-optimal |
| 355740.s1 | 355740s2 | \([0, -1, 0, -1543516, 692043640]\) | \(5726576/405\) | \(28761888281312229120\) | \([2]\) | \(9123840\) | \(2.4811\) |
Rank
sage: E.rank()
The elliptic curves in class 355740s have rank \(1\).
Complex multiplication
The elliptic curves in class 355740s do not have complex multiplication.Modular form 355740.2.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.
