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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 13552q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13552.y1 | 13552q1 | \([0, -1, 0, -10204, -401124]\) | \(-2141392/49\) | \(-2688917803264\) | \([]\) | \(31680\) | \(1.1726\) | \(\Gamma_0(N)\)-optimal |
13552.y2 | 13552q2 | \([0, -1, 0, 43036, -1785364]\) | \(160630448/117649\) | \(-6456091645636864\) | \([]\) | \(95040\) | \(1.7220\) |
Rank
sage: E.rank()
The elliptic curves in class 13552q have rank \(1\).
Complex multiplication
The elliptic curves in class 13552q do not have complex multiplication.Modular form 13552.2.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 Cremona 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 Cremona labels.