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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 13200bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13200.q3 | 13200bg1 | \([0, -1, 0, -557408, 160365312]\) | \(299270638153369/1069200\) | \(68428800000000\) | \([2]\) | \(92160\) | \(1.8727\) | \(\Gamma_0(N)\)-optimal |
| 13200.q2 | 13200bg2 | \([0, -1, 0, -565408, 155533312]\) | \(312341975961049/17862322500\) | \(1143188640000000000\) | \([2, 2]\) | \(184320\) | \(2.2193\) | |
| 13200.q1 | 13200bg3 | \([0, -1, 0, -1665408, -632066688]\) | \(7981893677157049/1917731420550\) | \(122734810915200000000\) | \([2]\) | \(368640\) | \(2.5658\) | |
| 13200.q4 | 13200bg4 | \([0, -1, 0, 406592, 633757312]\) | \(116149984977671/2779502343750\) | \(-177888150000000000000\) | \([2]\) | \(368640\) | \(2.5658\) |
Rank
sage: E.rank()
The elliptic curves in class 13200bg have rank \(0\).
Complex multiplication
The elliptic curves in class 13200bg do not have complex multiplication.Modular form 13200.2.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.
