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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 39984bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 39984.bl4 | 39984bs1 | \([0, -1, 0, 768, 2211840]\) | \(103823/4386816\) | \(-2113964095832064\) | \([2]\) | \(221184\) | \(1.6195\) | \(\Gamma_0(N)\)-optimal |
| 39984.bl3 | 39984bs2 | \([0, -1, 0, -250112, 47370240]\) | \(3590714269297/73410624\) | \(35375867916189696\) | \([2, 2]\) | \(442368\) | \(1.9661\) | |
| 39984.bl2 | 39984bs3 | \([0, -1, 0, -532352, -78847488]\) | \(34623662831857/14438442312\) | \(6957745355016142848\) | \([2]\) | \(884736\) | \(2.3127\) | |
| 39984.bl1 | 39984bs4 | \([0, -1, 0, -3981952, 3059711488]\) | \(14489843500598257/6246072\) | \(3009921534885888\) | \([2]\) | \(884736\) | \(2.3127\) |
Rank
sage: E.rank()
The elliptic curves in class 39984bs have rank \(1\).
Complex multiplication
The elliptic curves in class 39984bs do not have complex multiplication.Modular form 39984.2.a.bs
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.
