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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 2646.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2646.r1 | 2646bc2 | \([1, -1, 1, -104, -381]\) | \(-10353819/8\) | \(-95256\) | \([]\) | \(540\) | \(-0.11291\) | |
2646.r2 | 2646bc1 | \([1, -1, 1, 1, -3]\) | \(189/2\) | \(-2646\) | \([]\) | \(180\) | \(-0.66222\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2646.r have rank \(0\).
Complex multiplication
The elliptic curves in class 2646.r do not have complex multiplication.Modular form 2646.2.a.r
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.