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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 317680s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 317680.s4 | 317680s1 | \([0, 1, 0, -16365, 783838]\) | \(643956736/15125\) | \(11385103202000\) | \([2]\) | \(995328\) | \(1.2908\) | \(\Gamma_0(N)\)-optimal |
| 317680.s3 | 317680s2 | \([0, 1, 0, -36220, -1511400]\) | \(436334416/171875\) | \(2070018764000000\) | \([2]\) | \(1990656\) | \(1.6374\) | |
| 317680.s2 | 317680s3 | \([0, 1, 0, -160765, -24551142]\) | \(610462990336/8857805\) | \(6667571839219280\) | \([2]\) | \(2985984\) | \(1.8401\) | |
| 317680.s1 | 317680s4 | \([0, 1, 0, -2563220, -1580381000]\) | \(154639330142416/33275\) | \(400755632710400\) | \([2]\) | \(5971968\) | \(2.1867\) |
Rank
sage: E.rank()
The elliptic curves in class 317680s have rank \(1\).
Complex multiplication
The elliptic curves in class 317680s do not have complex multiplication.Modular form 317680.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
