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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 806f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
806.d1 | 806f1 | \([1, 1, 1, -14105, 638919]\) | \(-310345110881179921/11418002336\) | \(-11418002336\) | \([5]\) | \(1040\) | \(1.0174\) | \(\Gamma_0(N)\)-optimal |
806.d2 | 806f2 | \([1, 1, 1, 66885, 2264179]\) | \(33090970201326732239/21310335461500826\) | \(-21310335461500826\) | \([]\) | \(5200\) | \(1.8221\) |
Rank
sage: E.rank()
The elliptic curves in class 806f have rank \(0\).
Complex multiplication
The elliptic curves in class 806f do not have complex multiplication.Modular form 806.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.