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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 20160q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20160.dv1 | 20160q1 | \([0, 0, 0, -972, 5616]\) | \(78732/35\) | \(45148078080\) | \([2]\) | \(18432\) | \(0.74002\) | \(\Gamma_0(N)\)-optimal |
| 20160.dv2 | 20160q2 | \([0, 0, 0, 3348, 41904]\) | \(1608714/1225\) | \(-3160365465600\) | \([2]\) | \(36864\) | \(1.0866\) |
Rank
sage: E.rank()
The elliptic curves in class 20160q have rank \(0\).
Complex multiplication
The elliptic curves in class 20160q do not have complex multiplication.Modular form 20160.2.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.
