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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 32760a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32760.f2 | 32760a1 | \([0, 0, 0, -8343, -290358]\) | \(12745567728/147875\) | \(745119648000\) | \([2]\) | \(46080\) | \(1.0906\) | \(\Gamma_0(N)\)-optimal |
| 32760.f1 | 32760a2 | \([0, 0, 0, -15363, 269838]\) | \(19895760972/9953125\) | \(200609136000000\) | \([2]\) | \(92160\) | \(1.4372\) |
Rank
sage: E.rank()
The elliptic curves in class 32760a have rank \(1\).
Complex multiplication
The elliptic curves in class 32760a do not have complex multiplication.Modular form 32760.2.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 Cremona 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 Cremona labels.
