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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 2070.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2070.s1 | 2070r2 | \([1, -1, 1, -6782, 96981]\) | \(47316161414809/22001657400\) | \(16039208244600\) | \([2]\) | \(5376\) | \(1.2284\) | |
| 2070.s2 | 2070r1 | \([1, -1, 1, 1498, 10869]\) | \(510273943271/370215360\) | \(-269886997440\) | \([2]\) | \(2688\) | \(0.88179\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2070.s have rank \(0\).
Complex multiplication
The elliptic curves in class 2070.s do not have complex multiplication.Modular form 2070.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
