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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 35739r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35739.a3 | 35739r1 | \([0, 0, 1, -1083, 32580]\) | \(-4096/11\) | \(-377260919739\) | \([]\) | \(43200\) | \(0.90880\) | \(\Gamma_0(N)\)-optimal |
35739.a2 | 35739r2 | \([0, 0, 1, -33573, -4288590]\) | \(-122023936/161051\) | \(-5523477125898699\) | \([]\) | \(216000\) | \(1.7135\) | |
35739.a1 | 35739r3 | \([0, 0, 1, -25408263, -49295874780]\) | \(-52893159101157376/11\) | \(-377260919739\) | \([]\) | \(1080000\) | \(2.5182\) |
Rank
sage: E.rank()
The elliptic curves in class 35739r have rank \(1\).
Complex multiplication
The elliptic curves in class 35739r do not have complex multiplication.Modular form 35739.2.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.
\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.