Cremona's table of elliptic curves

3040 = 2⁵ · 5 · 19

Field	Data	Notes
Atkin-Lehner	2- 5+ 19-	Signs for the Atkin-Lehner involutions
Class	3040d	Isogeny class
Conductor	3040	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	1216000000 = 212 · 56 · 19	Discriminant
Eigenvalues	2-  0 5+ -2  4 -4  6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-268,-192]	[a1,a2,a3,a4,a6]
Generators	[-12:36:1]	Generators of the group modulo torsion
j	519718464/296875	j-invariant
L	2.9961871645744	L(r)(E,1)/r!
Ω	1.2777424580901	Real period
R	2.3449069455303	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	3040c2 6080s1 27360o2 15200e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3040d2

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
-	0	+	-2	4	-4	6	-	6	6	-8	-4	6	-2	-10	0	-4	-2	-16	-8	-2	-16	-6	-10	-12

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Quadratic twists for elliptic curve 3040d2

-4	8	-3	5	-19
3040c2	6080s1	27360o2	15200e2	57760d2

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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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