Cremona's table of elliptic curves

8547 = 3 · 7 · 11 · 37

Field	Data	Notes
Atkin-Lehner	3+ 7- 11+ 37+	Signs for the Atkin-Lehner involutions
Class	8547c	Isogeny class
Conductor	8547	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-2846151 = -1 · 33 · 7 · 11 · 372	Discriminant
Eigenvalues	-1 3+ -2 7- 11+ -2 -8  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,31,-34]	[a1,a2,a3,a4,a6]
Generators	[2:5:1] [10:32:1]	Generators of the group modulo torsion
j	3288008303/2846151	j-invariant
L	3.1120644896062	L(r)(E,1)/r!
Ω	1.4020908122498	Real period
R	4.4391767814425	Regulator
r	2	Rank of the group of rational points
S	0.99999999999992	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25641j1 59829j1 94017c1	Quadratic twists by: -3 -7 -11

Hecke Eigenvalues for elliptic curve 8547c1

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

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Quadratic twists for elliptic curve 8547c1

-3	-7	-11
25641j1	59829j1	94017c1

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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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