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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 167310.bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
167310.bq1 | 167310dg4 | \([1, -1, 0, -3455061804, 78169375649808]\) | \(1296294060988412126189641/647824320\) | \(2279527784224067520\) | \([2]\) | \(55738368\) | \(3.7587\) | |
167310.bq2 | 167310dg3 | \([1, -1, 0, -215940204, 1221450744528]\) | \(-316472948332146183241/7074906009600\) | \(-24894781380941406105600\) | \([2]\) | \(27869184\) | \(3.4121\) | |
167310.bq3 | 167310dg2 | \([1, -1, 0, -42736329, 106808747553]\) | \(2453170411237305241/19353090685500\) | \(68098567105670338165500\) | \([2]\) | \(18579456\) | \(3.2094\) | |
167310.bq4 | 167310dg1 | \([1, -1, 0, -908829, 3837808053]\) | \(-23592983745241/1794399750000\) | \(-6314032925052459750000\) | \([2]\) | \(9289728\) | \(2.8628\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 167310.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 167310.bq do not have complex multiplication.Modular form 167310.2.a.bq
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.