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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 268770r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
268770.r2 | 268770r1 | \([1, 0, 1, 646631, 885885692]\) | \(1238798620042199/14760960000000\) | \(-356293690506240000000\) | \([2]\) | \(12386304\) | \(2.6244\) | \(\Gamma_0(N)\)-optimal |
268770.r1 | 268770r2 | \([1, 0, 1, -10820889, 12779997436]\) | \(5805223604235668521/435937500000000\) | \(10522471485937500000000\) | \([2]\) | \(24772608\) | \(2.9710\) |
Rank
sage: E.rank()
The elliptic curves in class 268770r have rank \(0\).
Complex multiplication
The elliptic curves in class 268770r do not have complex multiplication.Modular form 268770.2.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.