Cremona's table of elliptic curves

29988 = 2² · 3² · 7² · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 17+	Signs for the Atkin-Lehner involutions
Class	29988k	Isogeny class
Conductor	29988	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	51840	Modular degree for the optimal curve
Δ	-3995201919744 = -1 · 28 · 33 · 76 · 173	Discriminant
Eigenvalues	2- 3+  3 7- -3  1 17+  7	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1176,97412]	[a1,a2,a3,a4,a6]
Generators	[28:-294:1]	Generators of the group modulo torsion
j	-221184/4913	j-invariant
L	6.9810177249911	L(r)(E,1)/r!
Ω	0.6568745675786	Real period
R	0.88563556239828	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	119952cs1 29988q2 612b1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 29988k1

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
-	+	3	-	-3	1	+	7	-3	-6	4	2	9	-1	-12	-12	-6	-2	-4	0	-8	14	-12	-6	16

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Quadratic twists for elliptic curve 29988k1

-4	-3	-7
119952cs1	29988q2	612b1

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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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