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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 91728.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91728.bg1 | 91728el4 | \([0, 0, 0, -13805211, -19738994870]\) | \(828279937799497/193444524\) | \(67956680508094070784\) | \([2]\) | \(3538944\) | \(2.7961\) | |
| 91728.bg2 | 91728el2 | \([0, 0, 0, -963291, -232118390]\) | \(281397674377/96589584\) | \(33931730733808287744\) | \([2, 2]\) | \(1769472\) | \(2.4495\) | |
| 91728.bg3 | 91728el1 | \([0, 0, 0, -398811, 94263946]\) | \(19968681097/628992\) | \(220963651502211072\) | \([2]\) | \(884736\) | \(2.1029\) | \(\Gamma_0(N)\)-optimal |
| 91728.bg4 | 91728el3 | \([0, 0, 0, 2846949, -1613711414]\) | \(7264187703863/7406095788\) | \(-2601746872283948433408\) | \([2]\) | \(3538944\) | \(2.7961\) |
Rank
sage: E.rank()
The elliptic curves in class 91728.bg have rank \(2\).
Complex multiplication
The elliptic curves in class 91728.bg do not have complex multiplication.Modular form 91728.2.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 LMFDB 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 LMFDB labels.
