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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 30960.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30960.l1 | 30960c4 | \([0, 0, 0, -71643, -235942]\) | \(54477543627364/31494140625\) | \(23510250000000000\) | \([2]\) | \(147456\) | \(1.8308\) | |
| 30960.l2 | 30960c2 | \([0, 0, 0, -48423, 4087622]\) | \(67283921459536/260015625\) | \(48525156000000\) | \([2, 2]\) | \(73728\) | \(1.4843\) | |
| 30960.l3 | 30960c1 | \([0, 0, 0, -48378, 4095623]\) | \(1073544204384256/16125\) | \(188082000\) | \([2]\) | \(36864\) | \(1.1377\) | \(\Gamma_0(N)\)-optimal |
| 30960.l4 | 30960c3 | \([0, 0, 0, -25923, 7899122]\) | \(-2580786074884/34615360125\) | \(-25840227871872000\) | \([2]\) | \(147456\) | \(1.8308\) |
Rank
sage: E.rank()
The elliptic curves in class 30960.l have rank \(0\).
Complex multiplication
The elliptic curves in class 30960.l do not have complex multiplication.Modular form 30960.2.a.l
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.
