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	21675r	Isogeny class
Conductor	21675	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	176256	Modular degree for the optimal curve
Δ	-5558806710796875 = -1 · 3 · 56 · 179	Discriminant
Eigenvalues	-2 3- 5+ -2 -5  1 17+ -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,40942,-1629706]	[a1,a2,a3,a4,a6]
j	4096/3	j-invariant
L	0.48032052478901	L(r)(E,1)/r!
Ω	0.24016026239451	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	65025bs1 867c1 21675h1	Quadratic twists by: -3 5 17

Hecke Eigenvalues for elliptic curve 21675r1

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
-2	-	+	-2	-5	1	+	-5	1	-6	10	2	-5	-1	2	-6	0	10	12	0	-6	-4	-6	-10	-8

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Quadratic twists for elliptic curve 21675r1

-3	5	17
65025bs1	867c1	21675h1

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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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