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SageMath
E = EllipticCurve("eu1")
E.isogeny_class()
Elliptic curves in class 78400eu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 78400.ds2 | 78400eu1 | \([0, -1, 0, -12833, 613537]\) | \(-9317\) | \(-25088000000000\) | \([]\) | \(122880\) | \(1.3095\) | \(\Gamma_0(N)\)-optimal |
| 78400.ds1 | 78400eu2 | \([0, -1, 0, -332932833, -2338096546463]\) | \(-162677523113838677\) | \(-25088000000000\) | \([]\) | \(4546560\) | \(3.1149\) |
Rank
sage: E.rank()
The elliptic curves in class 78400eu have rank \(1\).
Complex multiplication
The elliptic curves in class 78400eu do not have complex multiplication.Modular form 78400.2.a.eu
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.
\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
