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SageMath
E = EllipticCurve("dq1")
E.isogeny_class()
Elliptic curves in class 35280dq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35280.fx3 | 35280dq1 | \([0, 0, 0, -6027, 205114]\) | \(-1860867/320\) | \(-4163532226560\) | \([2]\) | \(69120\) | \(1.1477\) | \(\Gamma_0(N)\)-optimal |
| 35280.fx2 | 35280dq2 | \([0, 0, 0, -100107, 12190906]\) | \(8527173507/200\) | \(2602207641600\) | \([2]\) | \(138240\) | \(1.4943\) | |
| 35280.fx4 | 35280dq3 | \([0, 0, 0, 41013, -870534]\) | \(804357/500\) | \(-4742523426816000\) | \([2]\) | \(207360\) | \(1.6970\) | |
| 35280.fx1 | 35280dq4 | \([0, 0, 0, -170667, -7093926]\) | \(57960603/31250\) | \(296407714176000000\) | \([2]\) | \(414720\) | \(2.0436\) |
Rank
sage: E.rank()
The elliptic curves in class 35280dq have rank \(0\).
Complex multiplication
The elliptic curves in class 35280dq do not have complex multiplication.Modular form 35280.2.a.dq
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
