Show commands:
SageMath
E = EllipticCurve("eb1")
E.isogeny_class()
Elliptic curves in class 388080.eb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.eb1 | 388080eb1 | \([0, 0, 0, -1853523, 971089938]\) | \(74246873427/16940\) | \(160676693700526080\) | \([2]\) | \(7077888\) | \(2.2933\) | \(\Gamma_0(N)\)-optimal |
| 388080.eb2 | 388080eb2 | \([0, 0, 0, -1641843, 1201355442]\) | \(-51603494067/35870450\) | \(-340232898910863974400\) | \([2]\) | \(14155776\) | \(2.6399\) |
Rank
sage: E.rank()
The elliptic curves in class 388080.eb have rank \(1\).
Complex multiplication
The elliptic curves in class 388080.eb do not have complex multiplication.Modular form 388080.2.a.eb
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.
