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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 155526.bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
155526.bs1 | 155526bd2 | \([1, 1, 1, -4887, -133533]\) | \(-497971549873/6\) | \(-155526\) | \([]\) | \(127008\) | \(0.56017\) | |
155526.bs2 | 155526bd1 | \([1, 1, 1, -57, -225]\) | \(-790993/216\) | \(-5598936\) | \([]\) | \(42336\) | \(0.010869\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 155526.bs have rank \(0\).
Complex multiplication
The elliptic curves in class 155526.bs do not have complex multiplication.Modular form 155526.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.