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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 28611a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28611.x2 | 28611a1 | \([1, -1, 0, -24161610, -45553201177]\) | \(2393558463315519963/9284733153971\) | \(6050993953065191185473\) | \([2]\) | \(2764800\) | \(3.0376\) | \(\Gamma_0(N)\)-optimal |
| 28611.x1 | 28611a2 | \([1, -1, 0, -386225145, -2921423859682]\) | \(9776604686860471347243/147962546281\) | \(96429316597379934003\) | \([2]\) | \(5529600\) | \(3.3841\) |
Rank
sage: E.rank()
The elliptic curves in class 28611a have rank \(1\).
Complex multiplication
The elliptic curves in class 28611a do not have complex multiplication.Modular form 28611.2.a.a
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 Cremona 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 Cremona labels.
