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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 323400s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 323400.s2 | 323400s1 | \([0, -1, 0, -2009408, 2853346812]\) | \(-1389715708/4640625\) | \(-2996255319750000000000\) | \([2]\) | \(17031168\) | \(2.8072\) | \(\Gamma_0(N)\)-optimal |
| 323400.s1 | 323400s2 | \([0, -1, 0, -44884408, 115614596812]\) | \(7744223667854/11026125\) | \(14238205279452000000000\) | \([2]\) | \(34062336\) | \(3.1538\) |
Rank
sage: E.rank()
The elliptic curves in class 323400s have rank \(0\).
Complex multiplication
The elliptic curves in class 323400s do not have complex multiplication.Modular form 323400.2.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.
