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SageMath
E = EllipticCurve("et1")
E.isogeny_class()
Elliptic curves in class 134640et
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 134640.s2 | 134640et1 | \([0, 0, 0, -2883, 56018]\) | \(3550014724/238425\) | \(177983308800\) | \([2]\) | \(147456\) | \(0.90770\) | \(\Gamma_0(N)\)-optimal |
| 134640.s1 | 134640et2 | \([0, 0, 0, -9003, -260998]\) | \(54054018002/11570625\) | \(17274850560000\) | \([2]\) | \(294912\) | \(1.2543\) |
Rank
sage: E.rank()
The elliptic curves in class 134640et have rank \(2\).
Complex multiplication
The elliptic curves in class 134640et do not have complex multiplication.Modular form 134640.2.a.et
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.
