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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 21696by
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 21696.bv2 | 21696by1 | \([0, 1, 0, -106305, -13467969]\) | \(-506814405937489/4048994304\) | \(-1061419562827776\) | \([]\) | \(96768\) | \(1.7112\) | \(\Gamma_0(N)\)-optimal |
| 21696.bv1 | 21696by2 | \([0, 1, 0, -455745, 1314054591]\) | \(-39934705050538129/2823126576537804\) | \(-740065693279926091776\) | \([]\) | \(677376\) | \(2.6842\) |
Rank
sage: E.rank()
The elliptic curves in class 21696by have rank \(0\).
Complex multiplication
The elliptic curves in class 21696by do not have complex multiplication.Modular form 21696.2.a.by
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
