Cremona's table of elliptic curves

40368 = 2⁴ · 3 · 29²

Field	Data	Notes
Atkin-Lehner	2- 3- 29+	Signs for the Atkin-Lehner involutions
Class	40368bg	Isogeny class
Conductor	40368	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	11446189924589568 = 213 · 34 · 297	Discriminant
Eigenvalues	2- 3-  2  0 -4  6  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-4164912,3270182868]	[a1,a2,a3,a4,a6]
Generators	[130338:120801240:2197]	Generators of the group modulo torsion
j	3279392280793/4698	j-invariant
L	8.7638719195246	L(r)(E,1)/r!
Ω	0.34251278116028	Real period
R	6.3967480934835	Regulator
r	1	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	5046h3 121104ca4 1392h4	Quadratic twists by: -4 -3 29

Hecke Eigenvalues for elliptic curve 40368bg4

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	0	-4	6	2	4	0	+	-4	6	-6	-12	-8	-6	-8	-10	4	8	-2	4	0	-14	-18

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Quadratic twists for elliptic curve 40368bg4

-4	-3	29
5046h3	121104ca4	1392h4

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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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