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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 11760.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11760.m1 | 11760bn1 | \([0, -1, 0, -27701, 1783776]\) | \(1248870793216/42525\) | \(80048379600\) | \([2]\) | \(23040\) | \(1.1838\) | \(\Gamma_0(N)\)-optimal |
| 11760.m2 | 11760bn2 | \([0, -1, 0, -26476, 1947436]\) | \(-68150496976/14467005\) | \(-435719339838720\) | \([2]\) | \(46080\) | \(1.5304\) |
Rank
sage: E.rank()
The elliptic curves in class 11760.m have rank \(1\).
Complex multiplication
The elliptic curves in class 11760.m do not have complex multiplication.Modular form 11760.2.a.m
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.
