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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 11830x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11830.p4 | 11830x1 | \([1, 0, 0, -39465, 3010357]\) | \(1408317602329/2153060\) | \(10392409385540\) | \([2]\) | \(48384\) | \(1.3973\) | \(\Gamma_0(N)\)-optimal |
| 11830.p3 | 11830x2 | \([1, 0, 0, -51295, 1053675]\) | \(3092354182009/1689383150\) | \(8154329792868350\) | \([2]\) | \(96768\) | \(1.7439\) | |
| 11830.p2 | 11830x3 | \([1, 0, 0, -160300, -21774000]\) | \(94376601570889/12235496000\) | \(59058402212264000\) | \([2]\) | \(145152\) | \(1.9466\) | |
| 11830.p1 | 11830x4 | \([1, 0, 0, -2478980, -1502483048]\) | \(349046010201856969/7245875000\) | \(34974454662875000\) | \([2]\) | \(290304\) | \(2.2932\) |
Rank
sage: E.rank()
The elliptic curves in class 11830x have rank \(1\).
Complex multiplication
The elliptic curves in class 11830x do not have complex multiplication.Modular form 11830.2.a.x
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.
