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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 22743.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22743.e1 | 22743i1 | \([1, -1, 1, -20645, 1145684]\) | \(766060875/931\) | \(1182592310697\) | \([2]\) | \(46080\) | \(1.2268\) | \(\Gamma_0(N)\)-optimal |
| 22743.e2 | 22743i2 | \([1, -1, 1, -15230, 1756496]\) | \(-307546875/866761\) | \(-1100993441258907\) | \([2]\) | \(92160\) | \(1.5734\) |
Rank
sage: E.rank()
The elliptic curves in class 22743.e have rank \(1\).
Complex multiplication
The elliptic curves in class 22743.e do not have complex multiplication.Modular form 22743.2.a.e
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.
