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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 10710a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10710.c2 | 10710a1 | \([1, -1, 0, -259770, 63721396]\) | \(-71800566610391670267/23283051266048000\) | \(-628642384183296000\) | \([2]\) | \(150528\) | \(2.1278\) | \(\Gamma_0(N)\)-optimal |
10710.c1 | 10710a2 | \([1, -1, 0, -4437690, 3599077300]\) | \(357957021261376014720507/25088413952000000\) | \(677387176704000000\) | \([2]\) | \(301056\) | \(2.4744\) |
Rank
sage: E.rank()
The elliptic curves in class 10710a have rank \(0\).
Complex multiplication
The elliptic curves in class 10710a do not have complex multiplication.Modular form 10710.2.a.a
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.