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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 3264.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3264.r1 | 3264z2 | \([0, 1, 0, -237, 1329]\) | \(-23100424192/14739\) | \(-943296\) | \([]\) | \(864\) | \(0.087350\) | |
3264.r2 | 3264z1 | \([0, 1, 0, 3, 9]\) | \(32768/459\) | \(-29376\) | \([]\) | \(288\) | \(-0.46196\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3264.r have rank \(1\).
Complex multiplication
The elliptic curves in class 3264.r do not have complex multiplication.Modular form 3264.2.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.