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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 189618.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
189618.q1 | 189618bb1 | \([1, 0, 1, -33466, 2353496]\) | \(858729462625/38148\) | \(184133109732\) | \([2]\) | \(552960\) | \(1.2389\) | \(\Gamma_0(N)\)-optimal |
189618.q2 | 189618bb2 | \([1, 0, 1, -31776, 2602264]\) | \(-735091890625/181908738\) | \(-878038733757042\) | \([2]\) | \(1105920\) | \(1.5855\) |
Rank
sage: E.rank()
The elliptic curves in class 189618.q have rank \(0\).
Complex multiplication
The elliptic curves in class 189618.q do not have complex multiplication.Modular form 189618.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.