Cremona's table of elliptic curves

10164 = 2² · 3 · 7 · 11²

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 11+	Signs for the Atkin-Lehner involutions
Class	10164j	Isogeny class
Conductor	10164	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2880	Modular degree for the optimal curve
Δ	-447216 = -1 · 24 · 3 · 7 · 113	Discriminant
Eigenvalues	2- 3+ -3 7- 11+  1 -4 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-502,4501]	[a1,a2,a3,a4,a6]
Generators	[15:11:1]	Generators of the group modulo torsion
j	-658266368/21	j-invariant
L	2.9446459993125	L(r)(E,1)/r!
Ω	2.7703030830368	Real period
R	0.53146639754748	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	40656cc1 30492bb1 71148br1 10164c1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 10164j1

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
-	+	-3	-	+	1	-4	-5	4	5	2	1	-8	12	-7	6	-11	-2	3	8	11	-2	-8	-6	-12

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Quadratic twists for elliptic curve 10164j1

-4	-3	-7	-11
40656cc1	30492bb1	71148br1	10164c1

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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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