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SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 462462dv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
462462.dv2 | 462462dv1 | \([1, 0, 1, -8775044, 10004299358]\) | \(860833894093732321/8282804244\) | \(719001155495939316\) | \([]\) | \(19192320\) | \(2.5879\) | \(\Gamma_0(N)\)-optimal |
462462.dv1 | 462462dv2 | \([1, 0, 1, -282838834, -1830391836220]\) | \(28826282175168869972161/9077387406557184\) | \(787976130056044720766976\) | \([]\) | \(134346240\) | \(3.5609\) |
Rank
sage: E.rank()
The elliptic curves in class 462462dv have rank \(1\).
Complex multiplication
The elliptic curves in class 462462dv do not have complex multiplication.Modular form 462462.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.