Show commands:
SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 338130.bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 338130.bi1 | 338130bi1 | \([1, -1, 0, -485574, 110938868]\) | \(719564007681/114920000\) | \(2022165394090920000\) | \([2]\) | \(7077888\) | \(2.2350\) | \(\Gamma_0(N)\)-optimal |
| 338130.bi2 | 338130bi2 | \([1, -1, 0, 866946, 617592860]\) | \(4095232047999/11740625000\) | \(-206591416463615625000\) | \([2]\) | \(14155776\) | \(2.5816\) |
Rank
sage: E.rank()
The elliptic curves in class 338130.bi have rank \(1\).
Complex multiplication
The elliptic curves in class 338130.bi do not have complex multiplication.Modular form 338130.2.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.
