Cremona's table of elliptic curves

5684 = 2² · 7² · 29

Field	Data	Notes
Atkin-Lehner	2- 7- 29+	Signs for the Atkin-Lehner involutions
Class	5684g	Isogeny class
Conductor	5684	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-25329359104 = -1 · 28 · 76 · 292	Discriminant
Eigenvalues	2- -2  2 7- -6 -2 -2  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-212,-7820]	[a1,a2,a3,a4,a6]
Generators	[6372:62965:64]	Generators of the group modulo torsion
j	-35152/841	j-invariant
L	2.869425077459	L(r)(E,1)/r!
Ω	0.51635246477451	Real period
R	5.5571054138612	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	22736ba2 90944ce2 51156bc2 116c1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5684g2

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

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Quadratic twists for elliptic curve 5684g2

-4	8	-3	-7
22736ba2	90944ce2	51156bc2	116c1

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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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