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SageMath
E = EllipticCurve("de1")
E.isogeny_class()
Elliptic curves in class 92480de
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92480.bp2 | 92480de1 | \([0, -1, 0, 7379519, 2392880225]\) | \(7023836099951/4456448000\) | \(-28198258893104611328000\) | \([]\) | \(4644864\) | \(2.9968\) | \(\Gamma_0(N)\)-optimal |
| 92480.bp1 | 92480de2 | \([0, -1, 0, -122832321, 540918273121]\) | \(-32391289681150609/1228250000000\) | \(-7771775074107392000000000\) | \([]\) | \(13934592\) | \(3.5461\) |
Rank
sage: E.rank()
The elliptic curves in class 92480de have rank \(0\).
Complex multiplication
The elliptic curves in class 92480de do not have complex multiplication.Modular form 92480.2.a.de
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
