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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 41070r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41070.q1 | 41070r1 | \([1, 0, 1, -18973, 56888]\) | \(14910549714397/8599633920\) | \(435597256949760\) | \([2]\) | \(186624\) | \(1.4985\) | \(\Gamma_0(N)\)-optimal |
41070.q2 | 41070r2 | \([1, 0, 1, 75747, 473656]\) | \(948905782000163/550998028800\) | \(-27909703152806400\) | \([2]\) | \(373248\) | \(1.8451\) |
Rank
sage: E.rank()
The elliptic curves in class 41070r have rank \(0\).
Complex multiplication
The elliptic curves in class 41070r do not have complex multiplication.Modular form 41070.2.a.r
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.