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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 129960.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 129960.s1 | 129960r4 | \([0, 0, 0, -7928643, 8592694558]\) | \(784767874322/35625\) | \(2502268791287040000\) | \([2]\) | \(4423680\) | \(2.6065\) | |
| 129960.s2 | 129960r3 | \([0, 0, 0, -2470323, -1384022738]\) | \(23735908082/1954815\) | \(137304493115502458880\) | \([2]\) | \(4423680\) | \(2.6065\) | |
| 129960.s3 | 129960r2 | \([0, 0, 0, -520923, 119744422]\) | \(445138564/81225\) | \(2852586422067225600\) | \([2, 2]\) | \(2211840\) | \(2.2599\) | |
| 129960.s4 | 129960r1 | \([0, 0, 0, 63897, 10850938]\) | \(3286064/7695\) | \(-67561257364750080\) | \([2]\) | \(1105920\) | \(1.9133\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 129960.s have rank \(1\).
Complex multiplication
The elliptic curves in class 129960.s do not have complex multiplication.Modular form 129960.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
