Show commands:
SageMath
E = EllipticCurve("eu1")
E.isogeny_class()
Elliptic curves in class 92400eu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92400.ec2 | 92400eu1 | \([0, -1, 0, -162008, -39145488]\) | \(-7347774183121/6119866368\) | \(-391671447552000000\) | \([2]\) | \(1290240\) | \(2.0736\) | \(\Gamma_0(N)\)-optimal |
| 92400.ec1 | 92400eu2 | \([0, -1, 0, -2978008, -1976553488]\) | \(45637459887836881/13417633152\) | \(858728521728000000\) | \([2]\) | \(2580480\) | \(2.4202\) |
Rank
sage: E.rank()
The elliptic curves in class 92400eu have rank \(0\).
Complex multiplication
The elliptic curves in class 92400eu do not have complex multiplication.Modular form 92400.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
