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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 67600.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
67600.q1 | 67600bz1 | \([0, 1, 0, -1725208, -885986412]\) | \(-2941225/52\) | \(-10039762720000000000\) | \([]\) | \(1451520\) | \(2.4432\) | \(\Gamma_0(N)\)-optimal |
67600.q2 | 67600bz2 | \([0, 1, 0, 6724792, -4215286412]\) | \(174196775/140608\) | \(-27147518394880000000000\) | \([]\) | \(4354560\) | \(2.9925\) |
Rank
sage: E.rank()
The elliptic curves in class 67600.q have rank \(0\).
Complex multiplication
The elliptic curves in class 67600.q do not have complex multiplication.Modular form 67600.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.