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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 2646.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2646.bc1 | 2646q2 | \([1, -1, 1, -5081, 140753]\) | \(-10353819/8\) | \(-11206773144\) | \([3]\) | \(3780\) | \(0.86004\) | |
2646.bc2 | 2646q1 | \([1, -1, 1, 64, 809]\) | \(189/2\) | \(-311299254\) | \([]\) | \(1260\) | \(0.31074\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2646.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 2646.bc do not have complex multiplication.Modular form 2646.2.a.bc
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.