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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 14994.bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14994.bs1 | 14994cz2 | \([1, -1, 1, -168251, 26601635]\) | \(6141556990297/1019592\) | \(87446450842632\) | \([2]\) | \(73728\) | \(1.6832\) | |
14994.bs2 | 14994cz1 | \([1, -1, 1, -9491, 501491]\) | \(-1102302937/616896\) | \(-52908776980416\) | \([2]\) | \(36864\) | \(1.3366\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14994.bs have rank \(1\).
Complex multiplication
The elliptic curves in class 14994.bs do not have complex multiplication.Modular form 14994.2.a.bs
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.