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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 61710h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
61710.h1 | 61710h1 | \([1, 1, 0, -123937398, 530941818708]\) | \(118843307222596927933249/19794099600000000\) | \(35066454881475600000000\) | \([2]\) | \(16128000\) | \(3.3338\) | \(\Gamma_0(N)\)-optimal |
61710.h2 | 61710h2 | \([1, 1, 0, -111837398, 638760078708]\) | \(-87323024620536113533249/48975797371840020000\) | \(-86763612567854277671220000\) | \([2]\) | \(32256000\) | \(3.6804\) |
Rank
sage: E.rank()
The elliptic curves in class 61710h have rank \(1\).
Complex multiplication
The elliptic curves in class 61710h do not have complex multiplication.Modular form 61710.2.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 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.