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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 15480.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15480.b1 | 15480d3 | \([0, 0, 0, -71643, 235942]\) | \(54477543627364/31494140625\) | \(23510250000000000\) | \([2]\) | \(73728\) | \(1.8308\) | |
| 15480.b2 | 15480d2 | \([0, 0, 0, -48423, -4087622]\) | \(67283921459536/260015625\) | \(48525156000000\) | \([2, 2]\) | \(36864\) | \(1.4843\) | |
| 15480.b3 | 15480d1 | \([0, 0, 0, -48378, -4095623]\) | \(1073544204384256/16125\) | \(188082000\) | \([2]\) | \(18432\) | \(1.1377\) | \(\Gamma_0(N)\)-optimal |
| 15480.b4 | 15480d4 | \([0, 0, 0, -25923, -7899122]\) | \(-2580786074884/34615360125\) | \(-25840227871872000\) | \([2]\) | \(73728\) | \(1.8308\) |
Rank
sage: E.rank()
The elliptic curves in class 15480.b have rank \(1\).
Complex multiplication
The elliptic curves in class 15480.b do not have complex multiplication.Modular form 15480.2.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 LMFDB 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 LMFDB labels.
