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SageMath
E = EllipticCurve("dh1")
E.isogeny_class()
Elliptic curves in class 46800.dh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46800.dh1 | 46800cw8 | \([0, 0, 0, -468000075, -3896879687750]\) | \(242970740812818720001/24375\) | \(1137240000000000\) | \([2]\) | \(4718592\) | \(3.2366\) | |
| 46800.dh2 | 46800cw6 | \([0, 0, 0, -29250075, -60888437750]\) | \(59319456301170001/594140625\) | \(27720225000000000000\) | \([2, 2]\) | \(2359296\) | \(2.8900\) | |
| 46800.dh3 | 46800cw7 | \([0, 0, 0, -28548075, -63949859750]\) | \(-55150149867714721/5950927734375\) | \(-277646484375000000000000\) | \([2]\) | \(4718592\) | \(3.2366\) | |
| 46800.dh4 | 46800cw4 | \([0, 0, 0, -1872075, -903239750]\) | \(15551989015681/1445900625\) | \(67459939560000000000\) | \([2, 2]\) | \(1179648\) | \(2.5434\) | |
| 46800.dh5 | 46800cw2 | \([0, 0, 0, -414075, 86742250]\) | \(168288035761/27720225\) | \(1293314817600000000\) | \([2, 2]\) | \(589824\) | \(2.1969\) | |
| 46800.dh6 | 46800cw1 | \([0, 0, 0, -396075, 95940250]\) | \(147281603041/5265\) | \(245643840000000\) | \([2]\) | \(294912\) | \(1.8503\) | \(\Gamma_0(N)\)-optimal |
| 46800.dh7 | 46800cw3 | \([0, 0, 0, 755925, 488052250]\) | \(1023887723039/2798036865\) | \(-130545207973440000000\) | \([2]\) | \(1179648\) | \(2.5434\) | |
| 46800.dh8 | 46800cw5 | \([0, 0, 0, 2177925, -4276889750]\) | \(24487529386319/183539412225\) | \(-8563214816769600000000\) | \([2]\) | \(2359296\) | \(2.8900\) |
Rank
sage: E.rank()
The elliptic curves in class 46800.dh have rank \(1\).
Complex multiplication
The elliptic curves in class 46800.dh do not have complex multiplication.Modular form 46800.2.a.dh
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 16 & 16 & 8 \\ 2 & 1 & 2 & 2 & 4 & 8 & 8 & 4 \\ 4 & 2 & 1 & 4 & 8 & 16 & 16 & 8 \\ 4 & 2 & 4 & 1 & 2 & 4 & 4 & 2 \\ 8 & 4 & 8 & 2 & 1 & 2 & 2 & 4 \\ 16 & 8 & 16 & 4 & 2 & 1 & 4 & 8 \\ 16 & 8 & 16 & 4 & 2 & 4 & 1 & 8 \\ 8 & 4 & 8 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
