Cremona's table of elliptic curves

21675 = 3 · 5² · 17²

Field	Data	Notes
Atkin-Lehner	3- 5+ 17+	Signs for the Atkin-Lehner involutions
Class	21675p	Isogeny class
Conductor	21675	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-5558806710796875 = -1 · 3 · 56 · 179	Discriminant
Eigenvalues	0 3- 5+ -4  3  1 17+ -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-428683,-108234581]	[a1,a2,a3,a4,a6]
j	-23100424192/14739	j-invariant
L	1.6791569650757	L(r)(E,1)/r!
Ω	0.093286498059762	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	9	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	65025bi2 867a2 1275a2	Quadratic twists by: -3 5 17

Hecke Eigenvalues for elliptic curve 21675p2

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
0	-	+	-4	3	1	+	-1	9	-6	-2	-4	3	7	6	6	6	-8	4	-12	2	10	6	0	-16

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Quadratic twists for elliptic curve 21675p2

-3	5	17
65025bi2	867a2	1275a2

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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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