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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 59840.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59840.s1 | 59840v4 | \([0, 0, 0, -362828, 84119952]\) | \(40301032281655122/31112125\) | \(4077928448000\) | \([2]\) | \(270336\) | \(1.7274\) | |
| 59840.s2 | 59840v3 | \([0, 0, 0, -52748, -2809072]\) | \(123831683830962/45654296875\) | \(5984000000000000\) | \([2]\) | \(270336\) | \(1.7274\) | |
| 59840.s3 | 59840v2 | \([0, 0, 0, -22828, 1295952]\) | \(20074621850244/546390625\) | \(35808256000000\) | \([2, 2]\) | \(135168\) | \(1.3809\) | |
| 59840.s4 | 59840v1 | \([0, 0, 0, 292, 65968]\) | \(168055344/114841375\) | \(-1881561088000\) | \([2]\) | \(67584\) | \(1.0343\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 59840.s have rank \(0\).
Complex multiplication
The elliptic curves in class 59840.s do not have complex multiplication.Modular form 59840.2.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.
