Cremona's table of elliptic curves

29904 = 2⁴ · 3 · 7 · 89

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 89+	Signs for the Atkin-Lehner involutions
Class	29904d	Isogeny class
Conductor	29904	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	136235471437836288 = 212 · 33 · 712 · 89	Discriminant
Eigenvalues	2- 3-  2 7+ -4  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-244272,42860052]	[a1,a2,a3,a4,a6]
Generators	[45180:173166:125]	Generators of the group modulo torsion
j	393537938975182513/33260613144003	j-invariant
L	7.3742029731701	L(r)(E,1)/r!
Ω	0.31998114048455	Real period
R	7.6819141715699	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	1869b3 119616r3 89712x3	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 29904d3

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
-	-	2	+	-4	2	6	-4	-4	-6	0	-2	6	4	0	6	-4	-6	-12	16	-14	0	12	+	18

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Quadratic twists for elliptic curve 29904d3

-4	8	-3
1869b3	119616r3	89712x3

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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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