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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 51520q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 51520.ch2 | 51520q1 | \([0, -1, 0, -583681, 164685825]\) | \(83890194895342081/3958384640000\) | \(1037666783068160000\) | \([2]\) | \(860160\) | \(2.2177\) | \(\Gamma_0(N)\)-optimal |
| 51520.ch1 | 51520q2 | \([0, -1, 0, -1607681, -569931775]\) | \(1753007192038126081/478174101507200\) | \(125350471665503436800\) | \([2]\) | \(1720320\) | \(2.5643\) |
Rank
sage: E.rank()
The elliptic curves in class 51520q have rank \(1\).
Complex multiplication
The elliptic curves in class 51520q do not have complex multiplication.Modular form 51520.2.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.
