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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 179776.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
179776.q1 | 179776bb2 | \([0, -1, 0, -151297, 22703873]\) | \(-9814089221/1024\) | \(-39963865382912\) | \([]\) | \(599040\) | \(1.6420\) | |
179776.q2 | 179776bb1 | \([0, -1, 0, 1343, 1217]\) | \(6859/4\) | \(-156108849152\) | \([]\) | \(119808\) | \(0.83725\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 179776.q have rank \(0\).
Complex multiplication
The elliptic curves in class 179776.q do not have complex multiplication.Modular form 179776.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.