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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 21450.br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 21450.br1 | 21450bo4 | \([1, 1, 1, -56789313, -164744307969]\) | \(1296294060988412126189641/647824320\) | \(10122255000000\) | \([2]\) | \(995328\) | \(2.7316\) | |
| 21450.br2 | 21450bo3 | \([1, 1, 1, -3549313, -2575267969]\) | \(-316472948332146183241/7074906009600\) | \(-110545406400000000\) | \([2]\) | \(497664\) | \(2.3850\) | |
| 21450.br3 | 21450bo2 | \([1, 1, 1, -702438, -225342969]\) | \(2453170411237305241/19353090685500\) | \(302392041960937500\) | \([2]\) | \(331776\) | \(2.1823\) | |
| 21450.br4 | 21450bo1 | \([1, 1, 1, -14938, -8092969]\) | \(-23592983745241/1794399750000\) | \(-28037496093750000\) | \([2]\) | \(165888\) | \(1.8357\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 21450.br have rank \(0\).
Complex multiplication
The elliptic curves in class 21450.br do not have complex multiplication.Modular form 21450.2.a.br
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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
