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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 412224.bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
412224.bs1 | 412224bs1 | \([0, 1, 0, -31672545, -40482638721]\) | \(13403946614821979039929/5057590268826067968\) | \(1325816943431140761403392\) | \([2]\) | \(121405440\) | \(3.3282\) | \(\Gamma_0(N)\)-optimal |
412224.bs2 | 412224bs2 | \([0, 1, 0, 99082015, -288785548161]\) | \(410363075617640914325831/374944243169850027552\) | \(-98289383681517165622591488\) | \([2]\) | \(242810880\) | \(3.6748\) |
Rank
sage: E.rank()
The elliptic curves in class 412224.bs have rank \(1\).
Complex multiplication
The elliptic curves in class 412224.bs do not have complex multiplication.Modular form 412224.2.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.