Cremona's table of elliptic curves

429 = 3 · 11 · 13

Field	Data	Notes
Atkin-Lehner	3+ 11- 13-	Signs for the Atkin-Lehner involutions
Class	429a	Isogeny class
Conductor	429	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	61347 = 3 · 112 · 132	Discriminant
Eigenvalues	-1 3+  0  0 11- 13- -4 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-13,8]	[a1,a2,a3,a4,a6]
Generators	[-2:6:1]	Generators of the group modulo torsion
j	244140625/61347	j-invariant
L	1.1462496667886	L(r)(E,1)/r!
Ω	3.2842888784964	Real period
R	0.34901000161512	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6864v2 27456u2 1287c2 10725g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 429a2

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-1	+	0	0	-	-	-4	-8	0	4	-6	-6	6	-2	-8	6	0	-14	14	-4	6	-10	-12	12	-2

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Quadratic twists for elliptic curve 429a2

-4	8	-3	5	-7	-11	13	17
6864v2	27456u2	1287c2	10725g2	21021n2	4719c2	5577c2	123981p2

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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