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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 14784bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14784.bo3 | 14784bf1 | \([0, 1, 0, -2347889, -1385510865]\) | \(87364831012240243408/1760913\) | \(28850798592\) | \([2]\) | \(184320\) | \(1.9906\) | \(\Gamma_0(N)\)-optimal |
| 14784.bo2 | 14784bf2 | \([0, 1, 0, -2347969, -1385411809]\) | \(21843440425782779332/3100814593569\) | \(203214985204137984\) | \([2, 2]\) | \(368640\) | \(2.3371\) | |
| 14784.bo1 | 14784bf3 | \([0, 1, 0, -2560929, -1119339585]\) | \(14171198121996897746/4077720290568771\) | \(534474953925429952512\) | \([4]\) | \(737280\) | \(2.6837\) | |
| 14784.bo4 | 14784bf4 | \([0, 1, 0, -2136289, -1645143169]\) | \(-8226100326647904626/4152140742401883\) | \(-544229391388099608576\) | \([2]\) | \(737280\) | \(2.6837\) |
Rank
sage: E.rank()
The elliptic curves in class 14784bf have rank \(1\).
Complex multiplication
The elliptic curves in class 14784bf do not have complex multiplication.Modular form 14784.2.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.
