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sage:E = EllipticCurve([0, 0, 0, -2019, 36578])
E.isogeny_class()
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sage:E.rank()
The elliptic curve 154512.bg1 has
rank \(1\).
| |
| Bad L-factors: |
| Prime |
L-Factor |
| \(2\) | \(1\) |
| \(3\) | \(1\) |
| \(29\) | \(1 - T\) |
| \(37\) | \(1 - T\) |
|
| |
| Good L-factors: |
| Prime |
L-Factor |
Isogeny Class over \(\mathbb{F}_p\) |
| \(5\) |
\( 1 - 2 T + 5 T^{2}\) |
1.5.ac
|
| \(7\) |
\( 1 - 2 T + 7 T^{2}\) |
1.7.ac
|
| \(11\) |
\( 1 - 3 T + 11 T^{2}\) |
1.11.ad
|
| \(13\) |
\( 1 + 13 T^{2}\) |
1.13.a
|
| \(17\) |
\( 1 - 3 T + 17 T^{2}\) |
1.17.ad
|
| \(19\) |
\( 1 + 19 T^{2}\) |
1.19.a
|
| \(23\) |
\( 1 + 8 T + 23 T^{2}\) |
1.23.i
|
| $\cdots$ | $\cdots$ | $\cdots$ |
|
| |
| See L-function page for more information |
The elliptic curves in class 154512.bg 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 154512.bg
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sage:E.isogeny_class().curves
