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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 67270q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
67270.g2 | 67270q1 | \([1, 0, 1, -2423, -25494]\) | \(1702470121/686000\) | \(633535406000\) | \([3]\) | \(112320\) | \(0.96250\) | \(\Gamma_0(N)\)-optimal |
67270.g1 | 67270q2 | \([1, 0, 1, -170598, -27135304]\) | \(594559172575321/143360\) | \(132395970560\) | \([]\) | \(336960\) | \(1.5118\) |
Rank
sage: E.rank()
The elliptic curves in class 67270q have rank \(1\).
Complex multiplication
The elliptic curves in class 67270q do not have complex multiplication.Modular form 67270.2.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.