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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 418761bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 418761.bg3 | 418761bg1 | \([1, -1, 0, -9591, 354752]\) | \(5545233/161\) | \(2833002335961\) | \([2]\) | \(819200\) | \(1.1671\) | \(\Gamma_0(N)\)-optimal |
| 418761.bg2 | 418761bg2 | \([1, -1, 0, -22596, -802693]\) | \(72511713/25921\) | \(456113376089721\) | \([2, 2]\) | \(1638400\) | \(1.5137\) | |
| 418761.bg4 | 418761bg3 | \([1, -1, 0, 68439, -5700376]\) | \(2014698447/1958887\) | \(-34469139421637487\) | \([2]\) | \(3276800\) | \(1.8603\) | |
| 418761.bg1 | 418761bg4 | \([1, -1, 0, -321711, -70137550]\) | \(209267191953/55223\) | \(971719801234623\) | \([2]\) | \(3276800\) | \(1.8603\) |
Rank
sage: E.rank()
The elliptic curves in class 418761bg have rank \(0\).
Complex multiplication
The elliptic curves in class 418761bg do not have complex multiplication.Modular form 418761.2.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.
