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SageMath
sage: E = EllipticCurve("q1")
sage: E.isogeny_class()
Elliptic curves in class 3136.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
3136.q1 | 3136e3 | [0, 0, 0, -58604, -5460560] | [2] | 6144 | |
3136.q2 | 3136e4 | [0, 0, 0, -11564, 378672] | [2] | 6144 | |
3136.q3 | 3136e2 | [0, 0, 0, -3724, -82320] | [2, 2] | 3072 | |
3136.q4 | 3136e1 | [0, 0, 0, 196, -5488] | [2] | 1536 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3136.q have rank \(0\).
Complex multiplication
The elliptic curves in class 3136.q do not have complex multiplication.Modular form 3136.2.a.q
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.