Show commands:
SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 115920.ca
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.ca1 | 115920di1 | \([0, 0, 0, -17191803, 27435410602]\) | \(188191720927962271801/9422571110400\) | \(28135646574516633600\) | \([2]\) | \(5308416\) | \(2.8029\) | \(\Gamma_0(N)\)-optimal |
| 115920.ca2 | 115920di2 | \([0, 0, 0, -16270203, 30507472042]\) | \(-159520003524722950201/42335913815758080\) | \(-126414361279232574750720\) | \([2]\) | \(10616832\) | \(3.1494\) |
Rank
sage: E.rank()
The elliptic curves in class 115920.ca have rank \(0\).
Complex multiplication
The elliptic curves in class 115920.ca do not have complex multiplication.Modular form 115920.2.a.ca
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
