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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 4560a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4560.e4 | 4560a1 | \([0, -1, 0, 644, 14656]\) | \(115203799856/439833375\) | \(-112597344000\) | \([2]\) | \(4608\) | \(0.80338\) | \(\Gamma_0(N)\)-optimal |
| 4560.e3 | 4560a2 | \([0, -1, 0, -6576, 182160]\) | \(30716746229956/4112015625\) | \(4210704000000\) | \([2, 2]\) | \(9216\) | \(1.1500\) | |
| 4560.e2 | 4560a3 | \([0, -1, 0, -27096, -1525104]\) | \(1074299413481138/125244140625\) | \(256500000000000\) | \([2]\) | \(18432\) | \(1.4965\) | |
| 4560.e1 | 4560a4 | \([0, -1, 0, -101576, 12494160]\) | \(56594125707224978/1262172375\) | \(2584929024000\) | \([2]\) | \(18432\) | \(1.4965\) |
Rank
sage: E.rank()
The elliptic curves in class 4560a have rank \(1\).
Complex multiplication
The elliptic curves in class 4560a do not have complex multiplication.Modular form 4560.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
