Show commands:
SageMath
E = EllipticCurve("gh1")
E.isogeny_class()
Elliptic curves in class 286110.gh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 286110.gh1 | 286110gh1 | \([1, -1, 1, -266657, -53894811]\) | \(-119168121961/2524500\) | \(-44421828553624500\) | \([]\) | \(3317760\) | \(1.9848\) | \(\Gamma_0(N)\)-optimal |
| 286110.gh2 | 286110gh2 | \([1, -1, 1, 1098868, -243429681]\) | \(8339492177639/6277634880\) | \(-110463070058076098880\) | \([]\) | \(9953280\) | \(2.5341\) |
Rank
sage: E.rank()
The elliptic curves in class 286110.gh have rank \(0\).
Complex multiplication
The elliptic curves in class 286110.gh do not have complex multiplication.Modular form 286110.2.a.gh
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
