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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 156702.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
156702.h1 | 156702cr2 | \([1, 1, 0, -265611140, 1666265637072]\) | \(-17614662728794756493037625/2607524922260224512\) | \(-306772699578993153612288\) | \([]\) | \(33965568\) | \(3.5206\) | |
156702.h2 | 156702cr1 | \([1, 1, 0, 688915, 7356570789]\) | \(307348720697576375/198884536470802728\) | \(-23398566831253470146472\) | \([]\) | \(11321856\) | \(2.9713\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 156702.h have rank \(1\).
Complex multiplication
The elliptic curves in class 156702.h do not have complex multiplication.Modular form 156702.2.a.h
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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.