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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 33640f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33640.b2 | 33640f1 | \([0, 1, 0, -251, -1610]\) | \(4499456/25\) | \(9755600\) | \([2]\) | \(8960\) | \(0.18377\) | \(\Gamma_0(N)\)-optimal |
33640.b1 | 33640f2 | \([0, 1, 0, -396, 304]\) | \(1102736/625\) | \(3902240000\) | \([2]\) | \(17920\) | \(0.53034\) |
Rank
sage: E.rank()
The elliptic curves in class 33640f have rank \(1\).
Complex multiplication
The elliptic curves in class 33640f do not have complex multiplication.Modular form 33640.2.a.f
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.