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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 494190bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
494190.bd2 | 494190bd1 | \([1, -1, 0, 23355, 943445]\) | \(2161700757/1848320\) | \(-1204576691420160\) | \([2]\) | \(2949120\) | \(1.5813\) | \(\Gamma_0(N)\)-optimal* |
494190.bd1 | 494190bd2 | \([1, -1, 0, -115365, 8406581]\) | \(260549802603/104256800\) | \(67945654000418400\) | \([2]\) | \(5898240\) | \(1.9279\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 494190bd have rank \(0\).
Complex multiplication
The elliptic curves in class 494190bd do not have complex multiplication.Modular form 494190.2.a.bd
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.