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SageMath
E = EllipticCurve("de1")
E.isogeny_class()
Elliptic curves in class 78400.de
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 78400.de1 | 78400bu2 | \([0, -1, 0, -142753, 29218337]\) | \(-417267265/235298\) | \(-181420519600947200\) | \([]\) | \(663552\) | \(2.0148\) | |
| 78400.de2 | 78400bu1 | \([0, -1, 0, 14047, -542303]\) | \(397535/392\) | \(-302241598668800\) | \([]\) | \(221184\) | \(1.4655\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 78400.de have rank \(0\).
Complex multiplication
The elliptic curves in class 78400.de do not have complex multiplication.Modular form 78400.2.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 LMFDB 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 LMFDB labels.
