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SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 129360dv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
129360.l2 | 129360dv1 | \([0, -1, 0, 10519, 172656]\) | \(199344128/136125\) | \(-87890156046000\) | \([2]\) | \(322560\) | \(1.3642\) | \(\Gamma_0(N)\)-optimal |
129360.l1 | 129360dv2 | \([0, -1, 0, -46076, 1485660]\) | \(1047213232/515625\) | \(5326676124000000\) | \([2]\) | \(645120\) | \(1.7108\) |
Rank
sage: E.rank()
The elliptic curves in class 129360dv have rank \(1\).
Complex multiplication
The elliptic curves in class 129360dv do not have complex multiplication.Modular form 129360.2.a.dv
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.