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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 190575.cq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
190575.cq1 | 190575cn2 | \([0, 0, 1, -75900, -8048219]\) | \(35084566528/1029\) | \(1418235328125\) | \([]\) | \(497664\) | \(1.4315\) | |
190575.cq2 | 190575cn1 | \([0, 0, 1, -1650, 7906]\) | \(360448/189\) | \(260492203125\) | \([]\) | \(165888\) | \(0.88220\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 190575.cq have rank \(0\).
Complex multiplication
The elliptic curves in class 190575.cq do not have complex multiplication.Modular form 190575.2.a.cq
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.