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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 2160q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2160.o2 | 2160q1 | \([0, 0, 0, 3, 11]\) | \(6912/125\) | \(-54000\) | \([]\) | \(144\) | \(-0.41148\) | \(\Gamma_0(N)\)-optimal |
2160.o1 | 2160q2 | \([0, 0, 0, -297, 1971]\) | \(-9199872/5\) | \(-1574640\) | \([]\) | \(432\) | \(0.13782\) |
Rank
sage: E.rank()
The elliptic curves in class 2160q have rank \(1\).
Complex multiplication
The elliptic curves in class 2160q do not have complex multiplication.Modular form 2160.2.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.