Cremona's table of elliptic curves

7084 = 2² · 7 · 11 · 23

Field	Data	Notes
Atkin-Lehner	2- 7+ 11+ 23-	Signs for the Atkin-Lehner involutions
Class	7084b	Isogeny class
Conductor	7084	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	6240	Modular degree for the optimal curve
Δ	6637878016 = 28 · 7 · 115 · 23	Discriminant
Eigenvalues	2-  1  3 7+ 11+ -1  0 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-11044,443044]	[a1,a2,a3,a4,a6]
Generators	[60:2:1]	Generators of the group modulo torsion
j	581972233018192/25929211	j-invariant
L	5.444323071572	L(r)(E,1)/r!
Ω	1.2545960201503	Real period
R	1.4465009676767	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	28336bp1 113344u1 63756t1 49588g1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7084b1

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
-	1	3	+	+	-1	0	-1	-	-4	-4	4	-7	0	-13	-4	-12	0	3	10	13	4	1	-7	-3

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Quadratic twists for elliptic curve 7084b1

-4	8	-3	-7	-11
28336bp1	113344u1	63756t1	49588g1	77924v1

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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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