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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 83790g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 83790.a4 | 83790g1 | \([1, -1, 0, 98040, -14633984]\) | \(32807952226197/48013000000\) | \(-152514398799000000\) | \([2]\) | \(1492992\) | \(1.9826\) | \(\Gamma_0(N)\)-optimal |
| 83790.a3 | 83790g2 | \([1, -1, 0, -636960, -145904984]\) | \(8997224809453803/2305248169000\) | \(7322673829536387000\) | \([2]\) | \(2985984\) | \(2.3292\) | |
| 83790.a2 | 83790g3 | \([1, -1, 0, -949335, 596637341]\) | \(-40860428336307/42709811200\) | \(-98902480552191590400\) | \([2]\) | \(4478976\) | \(2.5320\) | |
| 83790.a1 | 83790g4 | \([1, -1, 0, -17883735, 29104006301]\) | \(273161111316733107/108726499840\) | \(251776353811965857280\) | \([2]\) | \(8957952\) | \(2.8785\) |
Rank
sage: E.rank()
The elliptic curves in class 83790g have rank \(0\).
Complex multiplication
The elliptic curves in class 83790g do not have complex multiplication.Modular form 83790.2.a.g
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.
