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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 51600cx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 51600.dv3 | 51600cx1 | \([0, 1, 0, -27408, 1735188]\) | \(35578826569/51600\) | \(3302400000000\) | \([2]\) | \(110592\) | \(1.3042\) | \(\Gamma_0(N)\)-optimal |
| 51600.dv2 | 51600cx2 | \([0, 1, 0, -35408, 631188]\) | \(76711450249/41602500\) | \(2662560000000000\) | \([2, 2]\) | \(221184\) | \(1.6508\) | |
| 51600.dv4 | 51600cx3 | \([0, 1, 0, 136592, 5103188]\) | \(4403686064471/2721093750\) | \(-174150000000000000\) | \([2]\) | \(442368\) | \(1.9974\) | |
| 51600.dv1 | 51600cx4 | \([0, 1, 0, -335408, -74368812]\) | \(65202655558249/512820150\) | \(32820489600000000\) | \([2]\) | \(442368\) | \(1.9974\) |
Rank
sage: E.rank()
The elliptic curves in class 51600cx have rank \(1\).
Complex multiplication
The elliptic curves in class 51600cx do not have complex multiplication.Modular form 51600.2.a.cx
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
