Cremona's table of elliptic curves

8784 = 2⁴ · 3² · 61

Field	Data	Notes
Atkin-Lehner	2- 3- 61+	Signs for the Atkin-Lehner involutions
Class	8784q	Isogeny class
Conductor	8784	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-2914320384 = -1 · 216 · 36 · 61	Discriminant
Eigenvalues	2- 3- -1  5 -3 -3  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,357,74]	[a1,a2,a3,a4,a6]
Generators	[7:54:1]	Generators of the group modulo torsion
j	1685159/976	j-invariant
L	4.5790775506445	L(r)(E,1)/r!
Ω	0.85623910682885	Real period
R	1.3369739580114	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	1098j1 35136ck1 976a1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 8784q1

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	5	-3	-3	0	0	5	-6	0	-12	3	8	12	2	-9	+	-7	-16	-3	-1	-12	-12	2

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Quadratic twists for elliptic curve 8784q1

-4	8	-3
1098j1	35136ck1	976a1

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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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