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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 11760.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11760.a1 | 11760g1 | \([0, -1, 0, -2249851, 1299659026]\) | \(1950665639360512/492075\) | \(317712018632400\) | \([2]\) | \(161280\) | \(2.1577\) | \(\Gamma_0(N)\)-optimal |
| 11760.a2 | 11760g2 | \([0, -1, 0, -2241276, 1310048496]\) | \(-120527903507632/1937102445\) | \(-20011282120772893440\) | \([2]\) | \(322560\) | \(2.5042\) |
Rank
sage: E.rank()
The elliptic curves in class 11760.a have rank \(0\).
Complex multiplication
The elliptic curves in class 11760.a do not have complex multiplication.Modular form 11760.2.a.a
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.
