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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 6480.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6480.a1 | 6480n1 | \([0, 0, 0, -70203, -7159702]\) | \(-115330920751809/4096000\) | \(-1358954496000\) | \([]\) | \(25920\) | \(1.4176\) | \(\Gamma_0(N)\)-optimal |
| 6480.a2 | 6480n2 | \([0, 0, 0, -16443, -17764758]\) | \(-225866529/62500000\) | \(-136048896000000000\) | \([]\) | \(77760\) | \(1.9669\) |
Rank
sage: E.rank()
The elliptic curves in class 6480.a have rank \(0\).
Complex multiplication
The elliptic curves in class 6480.a do not have complex multiplication.Modular form 6480.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
