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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 23520.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23520.a1 | 23520bi1 | \([0, -1, 0, -67146, -6674604]\) | \(4446542056384/25725\) | \(193697313600\) | \([2]\) | \(92160\) | \(1.3561\) | \(\Gamma_0(N)\)-optimal |
| 23520.a2 | 23520bi2 | \([0, -1, 0, -65921, -6931119]\) | \(-65743598656/5294205\) | \(-2551226056888320\) | \([2]\) | \(184320\) | \(1.7027\) |
Rank
sage: E.rank()
The elliptic curves in class 23520.a have rank \(1\).
Complex multiplication
The elliptic curves in class 23520.a do not have complex multiplication.Modular form 23520.2.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.
