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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 397800cx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 397800.cx1 | 397800cx1 | \([0, 0, 0, -21982575, 38483055250]\) | \(402876451435348816/13746755117745\) | \(40085537923344420000000\) | \([2]\) | \(35389440\) | \(3.1091\) | \(\Gamma_0(N)\)-optimal |
| 397800.cx2 | 397800cx2 | \([0, 0, 0, 7541925, 134171959750]\) | \(4067455675907516/669098843633025\) | \(-7804368912135603600000000\) | \([2]\) | \(70778880\) | \(3.4557\) |
Rank
sage: E.rank()
The elliptic curves in class 397800cx have rank \(0\).
Complex multiplication
The elliptic curves in class 397800cx do not have complex multiplication.Modular form 397800.2.a.cx
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.
