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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 92778.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92778.x1 | 92778bd2 | \([1, 0, 0, -2077634, 1139795184]\) | \(9552945120036912719/121083580434348\) | \(12571260571435312404\) | \([2]\) | \(2580480\) | \(2.4739\) | |
| 92778.x2 | 92778bd1 | \([1, 0, 0, -21854, 46531380]\) | \(-11117936687759/9003384318096\) | \(-934758370057681008\) | \([2]\) | \(1290240\) | \(2.1273\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92778.x have rank \(1\).
Complex multiplication
The elliptic curves in class 92778.x do not have complex multiplication.Modular form 92778.2.a.x
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.
