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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 13200b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13200.s3 | 13200b1 | \([0, -1, 0, -1383, 20262]\) | \(1171019776/165\) | \(41250000\) | \([2]\) | \(6144\) | \(0.47770\) | \(\Gamma_0(N)\)-optimal |
| 13200.s2 | 13200b2 | \([0, -1, 0, -1508, 16512]\) | \(94875856/27225\) | \(108900000000\) | \([2, 2]\) | \(12288\) | \(0.82427\) | |
| 13200.s1 | 13200b3 | \([0, -1, 0, -9008, -313488]\) | \(5052857764/219615\) | \(3513840000000\) | \([2]\) | \(24576\) | \(1.1708\) | |
| 13200.s4 | 13200b4 | \([0, -1, 0, 3992, 104512]\) | \(439608956/556875\) | \(-8910000000000\) | \([2]\) | \(24576\) | \(1.1708\) |
Rank
sage: E.rank()
The elliptic curves in class 13200b have rank \(1\).
Complex multiplication
The elliptic curves in class 13200b do not have complex multiplication.Modular form 13200.2.a.b
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
