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SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 185130dv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
185130.d2 | 185130dv1 | \([1, -1, 0, -765, 4725]\) | \(51064811/20400\) | \(19794099600\) | \([2]\) | \(184320\) | \(0.67388\) | \(\Gamma_0(N)\)-optimal |
185130.d1 | 185130dv2 | \([1, -1, 0, -10665, 426465]\) | \(138268615211/52020\) | \(50474953980\) | \([2]\) | \(368640\) | \(1.0205\) |
Rank
sage: E.rank()
The elliptic curves in class 185130dv have rank \(2\).
Complex multiplication
The elliptic curves in class 185130dv do not have complex multiplication.Modular form 185130.2.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.