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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 44880bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44880.g3 | 44880bf1 | \([0, -1, 0, -42416, -3347520]\) | \(2060455000819249/517017600\) | \(2117704089600\) | \([2]\) | \(110592\) | \(1.3521\) | \(\Gamma_0(N)\)-optimal |
| 44880.g2 | 44880bf2 | \([0, -1, 0, -47536, -2483264]\) | \(2900285849172529/1019696040000\) | \(4176674979840000\) | \([2, 2]\) | \(221184\) | \(1.6987\) | |
| 44880.g4 | 44880bf3 | \([0, -1, 0, 142544, -17537600]\) | \(78200142092480591/77517928125000\) | \(-317513433600000000\) | \([2]\) | \(442368\) | \(2.0452\) | |
| 44880.g1 | 44880bf4 | \([0, -1, 0, -319536, 67801536]\) | \(880895732965860529/26454814115400\) | \(108358918616678400\) | \([2]\) | \(442368\) | \(2.0452\) |
Rank
sage: E.rank()
The elliptic curves in class 44880bf have rank \(1\).
Complex multiplication
The elliptic curves in class 44880bf do not have complex multiplication.Modular form 44880.2.a.bf
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.
