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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 3024q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3024.e2 | 3024q1 | \([0, 0, 0, 81, -54]\) | \(11664/7\) | \(-35271936\) | \([]\) | \(864\) | \(0.13750\) | \(\Gamma_0(N)\)-optimal |
3024.e1 | 3024q2 | \([0, 0, 0, -999, 13554]\) | \(-2431344/343\) | \(-15554923776\) | \([]\) | \(2592\) | \(0.68680\) |
Rank
sage: E.rank()
The elliptic curves in class 3024q have rank \(0\).
Complex multiplication
The elliptic curves in class 3024q do not have complex multiplication.Modular form 3024.2.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.