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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 14784.bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14784.bq1 | 14784cq3 | \([0, 1, 0, -2575809, -1592036289]\) | \(7209828390823479793/49509306\) | \(12978567512064\) | \([2]\) | \(147456\) | \(2.1160\) | |
14784.bq2 | 14784cq4 | \([0, 1, 0, -224449, -3556033]\) | \(4770223741048753/2740574865798\) | \(718425257619750912\) | \([2]\) | \(147456\) | \(2.1160\) | |
14784.bq3 | 14784cq2 | \([0, 1, 0, -161089, -24883009]\) | \(1763535241378513/4612311396\) | \(1209089758593024\) | \([2, 2]\) | \(73728\) | \(1.7694\) | |
14784.bq4 | 14784cq1 | \([0, 1, 0, -6209, -690753]\) | \(-100999381393/723148272\) | \(-189568980615168\) | \([2]\) | \(36864\) | \(1.4228\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14784.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 14784.bq do not have complex multiplication.Modular form 14784.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.