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sage:E = EllipticCurve([1, -1, 0, -1629792420147, 800841856848673653])
E.isogeny_class()
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sage:E.rank()
The elliptic curve 43434e1 has
rank \(1\).
| |
| Bad L-factors: |
| Prime |
L-Factor |
| \(2\) | \(1 + T\) |
| \(3\) | \(1\) |
| \(19\) | \(1 - T\) |
| \(127\) | \(1 + T\) |
|
| |
| Good L-factors: |
| Prime |
L-Factor |
Isogeny Class over \(\mathbb{F}_p\) |
| \(5\) |
\( 1 + 5 T^{2}\) |
1.5.a
|
| \(7\) |
\( 1 - T + 7 T^{2}\) |
1.7.ab
|
| \(11\) |
\( 1 + 11 T^{2}\) |
1.11.a
|
| \(13\) |
\( 1 + T + 13 T^{2}\) |
1.13.b
|
| \(17\) |
\( 1 - T + 17 T^{2}\) |
1.17.ab
|
| \(23\) |
\( 1 - 3 T + 23 T^{2}\) |
1.23.ad
|
| \(29\) |
\( 1 + T + 29 T^{2}\) |
1.29.b
|
| $\cdots$ | $\cdots$ | $\cdots$ |
|
| |
| See L-function page for more information |
The elliptic curves in class 43434e do not have complex multiplication.
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sage:E.q_eigenform(10)
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sage:E.isogeny_graph().plot(edge_labels=True)
Elliptic curves in class 43434e
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sage:E.isogeny_class().curves
