Cremona's table of elliptic curves

38808 = 2³ · 3² · 7² · 11

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 11+	Signs for the Atkin-Lehner involutions
Class	38808w	Isogeny class
Conductor	38808	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	286720	Modular degree for the optimal curve
Δ	-32804824963857408 = -1 · 210 · 38 · 79 · 112	Discriminant
Eigenvalues	2+ 3- -2 7- 11+  4  2  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-81291,-12470794]	[a1,a2,a3,a4,a6]
Generators	[7103530:218429946:6859]	Generators of the group modulo torsion
j	-1972156/1089	j-invariant
L	4.9461199841194	L(r)(E,1)/r!
Ω	0.13783056056352	Real period
R	8.9713775448246	Regulator
r	1	Rank of the group of rational points
S	0.99999999999973	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	77616cl1 12936s1 38808u1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 38808w1

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	2	-8	6	-6	2	-6	4	6	14	-8	4	8	-16	14	-4	-14	-12	-16

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Quadratic twists for elliptic curve 38808w1

-4	-3	-7
77616cl1	12936s1	38808u1

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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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