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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 18032q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18032.k2 | 18032q1 | \([0, 0, 0, -7987, -318990]\) | \(-116930169/23552\) | \(-11349480439808\) | \([2]\) | \(34560\) | \(1.2276\) | \(\Gamma_0(N)\)-optimal |
18032.k1 | 18032q2 | \([0, 0, 0, -133427, -18758670]\) | \(545138290809/16928\) | \(8157439066112\) | \([2]\) | \(69120\) | \(1.5742\) |
Rank
sage: E.rank()
The elliptic curves in class 18032q have rank \(1\).
Complex multiplication
The elliptic curves in class 18032q do not have complex multiplication.Modular form 18032.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.