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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 8280.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8280.q1 | 8280p2 | \([0, 0, 0, -2187, 17766]\) | \(28697814/13225\) | \(533110118400\) | \([2]\) | \(7680\) | \(0.94490\) | |
8280.q2 | 8280p1 | \([0, 0, 0, -1107, -13986]\) | \(7443468/115\) | \(2317870080\) | \([2]\) | \(3840\) | \(0.59833\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8280.q have rank \(1\).
Complex multiplication
The elliptic curves in class 8280.q do not have complex multiplication.Modular form 8280.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.