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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 5808bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5808.t3 | 5808bg1 | \([0, 1, 0, -12624, -545580]\) | \(30664297/297\) | \(2155125215232\) | \([2]\) | \(11520\) | \(1.1863\) | \(\Gamma_0(N)\)-optimal |
| 5808.t2 | 5808bg2 | \([0, 1, 0, -22304, 395316]\) | \(169112377/88209\) | \(640072188923904\) | \([2, 2]\) | \(23040\) | \(1.5329\) | |
| 5808.t1 | 5808bg3 | \([0, 1, 0, -283664, 57999060]\) | \(347873904937/395307\) | \(2868471661473792\) | \([2]\) | \(46080\) | \(1.8795\) | |
| 5808.t4 | 5808bg4 | \([0, 1, 0, 84176, 3163796]\) | \(9090072503/5845851\) | \(-42419329611411456\) | \([4]\) | \(46080\) | \(1.8795\) |
Rank
sage: E.rank()
The elliptic curves in class 5808bg have rank \(0\).
Complex multiplication
The elliptic curves in class 5808bg do not have complex multiplication.Modular form 5808.2.a.bg
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
