Show commands:
SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 190575.bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 190575.bi1 | 190575bn2 | \([1, -1, 1, -1402655, 590591972]\) | \(15124197817/1294139\) | \(26114672905213921875\) | \([2]\) | \(4423680\) | \(2.4670\) | |
| 190575.bi2 | 190575bn1 | \([1, -1, 1, 94720, 42552722]\) | \(4657463/41503\) | \(-837496798709484375\) | \([2]\) | \(2211840\) | \(2.1204\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 190575.bi have rank \(1\).
Complex multiplication
The elliptic curves in class 190575.bi do not have complex multiplication.Modular form 190575.2.a.bi
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.
