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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 60648.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 60648.s1 | 60648v4 | \([0, -1, 0, -54992, -4938948]\) | \(381775972/567\) | \(27315214875648\) | \([2]\) | \(221184\) | \(1.4792\) | |
| 60648.s2 | 60648v2 | \([0, -1, 0, -4452, -26460]\) | \(810448/441\) | \(5311291781376\) | \([2, 2]\) | \(110592\) | \(1.1326\) | |
| 60648.s3 | 60648v1 | \([0, -1, 0, -2647, 52960]\) | \(2725888/21\) | \(15807416016\) | \([2]\) | \(55296\) | \(0.78603\) | \(\Gamma_0(N)\)-optimal |
| 60648.s4 | 60648v3 | \([0, -1, 0, 17208, -225732]\) | \(11696828/7203\) | \(-347004396383232\) | \([2]\) | \(221184\) | \(1.4792\) |
Rank
sage: E.rank()
The elliptic curves in class 60648.s have rank \(1\).
Complex multiplication
The elliptic curves in class 60648.s do not have complex multiplication.Modular form 60648.2.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 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.
