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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 39600.ct
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 39600.ct1 | 39600dq4 | \([0, 0, 0, -14988675, 17080789250]\) | \(7981893677157049/1917731420550\) | \(89473677157180800000000\) | \([2]\) | \(2949120\) | \(3.1152\) | |
| 39600.ct2 | 39600dq2 | \([0, 0, 0, -5088675, -4194310750]\) | \(312341975961049/17862322500\) | \(833384518560000000000\) | \([2, 2]\) | \(1474560\) | \(2.7686\) | |
| 39600.ct3 | 39600dq1 | \([0, 0, 0, -5016675, -4324846750]\) | \(299270638153369/1069200\) | \(49884595200000000\) | \([2]\) | \(737280\) | \(2.4220\) | \(\Gamma_0(N)\)-optimal |
| 39600.ct4 | 39600dq3 | \([0, 0, 0, 3659325, -17115106750]\) | \(116149984977671/2779502343750\) | \(-129680461350000000000000\) | \([2]\) | \(2949120\) | \(3.1152\) |
Rank
sage: E.rank()
The elliptic curves in class 39600.ct have rank \(0\).
Complex multiplication
The elliptic curves in class 39600.ct do not have complex multiplication.Modular form 39600.2.a.ct
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
