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SageMath
E = EllipticCurve("fu1")
E.isogeny_class()
Elliptic curves in class 85680fu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
85680.fs2 | 85680fu1 | \([0, 0, 0, -242427, -120140246]\) | \(-527690404915129/1782829440000\) | \(-5323500182568960000\) | \([2]\) | \(1474560\) | \(2.2794\) | \(\Gamma_0(N)\)-optimal |
85680.fs1 | 85680fu2 | \([0, 0, 0, -5426427, -4859353046]\) | \(5918043195362419129/8515734343200\) | \(25427846497045708800\) | \([2]\) | \(2949120\) | \(2.6260\) |
Rank
sage: E.rank()
The elliptic curves in class 85680fu have rank \(0\).
Complex multiplication
The elliptic curves in class 85680fu do not have complex multiplication.Modular form 85680.2.a.fu
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.