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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 4840.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4840.a1 | 4840e2 | \([0, 1, 0, -26176, -1595376]\) | \(821516/25\) | \(60363460889600\) | \([2]\) | \(12672\) | \(1.4204\) | |
| 4840.a2 | 4840e1 | \([0, 1, 0, 444, -83360]\) | \(16/5\) | \(-3018173044480\) | \([2]\) | \(6336\) | \(1.0738\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4840.a have rank \(0\).
Complex multiplication
The elliptic curves in class 4840.a do not have complex multiplication.Modular form 4840.2.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 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.
