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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 242760r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 242760.r2 | 242760r1 | \([0, -1, 0, -5119731, 4454570100]\) | \(38428347995170816/59267578125\) | \(22889204103281250000\) | \([2]\) | \(8847360\) | \(2.6140\) | \(\Gamma_0(N)\)-optimal |
| 242760.r1 | 242760r2 | \([0, -1, 0, -81885356, 285232520100]\) | \(9826728297992948176/23428125\) | \(144767483834400000\) | \([2]\) | \(17694720\) | \(2.9606\) |
Rank
sage: E.rank()
The elliptic curves in class 242760r have rank \(1\).
Complex multiplication
The elliptic curves in class 242760r do not have complex multiplication.Modular form 242760.2.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.
