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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 90480bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 90480.v4 | 90480bg1 | \([0, -1, 0, -453040, -33485888]\) | \(2510581756496128561/1333551278592000\) | \(5462226037112832000\) | \([2]\) | \(1658880\) | \(2.2868\) | \(\Gamma_0(N)\)-optimal |
| 90480.v2 | 90480bg2 | \([0, -1, 0, -4185520, 3271998400]\) | \(1979758117698975186481/17510434929000000\) | \(71722741469184000000\) | \([2, 2]\) | \(3317760\) | \(2.6334\) | |
| 90480.v3 | 90480bg3 | \([0, -1, 0, -1265200, 7750601152]\) | \(-54681655838565466801/6303365630859375000\) | \(-25818585624000000000000\) | \([4]\) | \(6635520\) | \(2.9799\) | |
| 90480.v1 | 90480bg4 | \([0, -1, 0, -66825520, 210284670400]\) | \(8057323694463985606146481/638717154543000\) | \(2616185465008128000\) | \([2]\) | \(6635520\) | \(2.9799\) |
Rank
sage: E.rank()
The elliptic curves in class 90480bg have rank \(0\).
Complex multiplication
The elliptic curves in class 90480bg do not have complex multiplication.Modular form 90480.2.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.
