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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 36980a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 36980.a3 | 36980a1 | \([0, -1, 0, -2465, -31570]\) | \(16384/5\) | \(505709043920\) | \([2]\) | \(38556\) | \(0.95065\) | \(\Gamma_0(N)\)-optimal |
| 36980.a4 | 36980a2 | \([0, -1, 0, 6780, -220168]\) | \(21296/25\) | \(-40456723513600\) | \([2]\) | \(77112\) | \(1.2972\) | |
| 36980.a1 | 36980a3 | \([0, -1, 0, -76425, 8155802]\) | \(488095744/125\) | \(12642726098000\) | \([2]\) | \(115668\) | \(1.5000\) | |
| 36980.a2 | 36980a4 | \([0, -1, 0, -67180, 10193400]\) | \(-20720464/15625\) | \(-25285452196000000\) | \([2]\) | \(231336\) | \(1.8465\) |
Rank
sage: E.rank()
The elliptic curves in class 36980a have rank \(0\).
Complex multiplication
The elliptic curves in class 36980a do not have complex multiplication.Modular form 36980.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
