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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 265200r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
265200.r1 | 265200r1 | \([0, -1, 0, -2442508, 1426112512]\) | \(402876451435348816/13746755117745\) | \(54987020470980000000\) | \([2]\) | \(8847360\) | \(2.5598\) | \(\Gamma_0(N)\)-optimal |
265200.r2 | 265200r2 | \([0, -1, 0, 837992, 4969052512]\) | \(4067455675907516/669098843633025\) | \(-10705581498128400000000\) | \([2]\) | \(17694720\) | \(2.9064\) |
Rank
sage: E.rank()
The elliptic curves in class 265200r have rank \(1\).
Complex multiplication
The elliptic curves in class 265200r do not have complex multiplication.Modular form 265200.2.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.