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	429b	Isogeny class
Conductor	429	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	108679952667 = 3 · 118 · 132	Discriminant
Eigenvalues	-1 3- -2  0 11+ 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-3009,-61770]	[a1,a2,a3,a4,a6]
Generators	[-34:56:1]	Generators of the group modulo torsion
j	3013001140430737/108679952667	j-invariant
L	1.3666547477462	L(r)(E,1)/r!
Ω	0.64603402715145	Real period
R	2.1154531964395	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	6864r5 27456p6 1287e5 10725a5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 429b5

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	-	-2	0	+	-	-6	-4	-8	-10	0	6	10	4	8	-10	-12	14	-12	0	-6	8	12	2	-14

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Quadratic twists for elliptic curve 429b5

-4	8	-3	5	-7	-11	13	17
6864r5	27456p6	1287e5	10725a5	21021b6	4719j5	5577g5	123981h6

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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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