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	21675t	Isogeny class
Conductor	21675	Conductor
∏ cp	27	Product of Tamagawa factors cp
deg	13608	Modular degree for the optimal curve
Δ	41098596075 = 39 · 52 · 174	Discriminant
Eigenvalues	-1 3- 5+  2 -4  1 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-873,1782]	[a1,a2,a3,a4,a6]
Generators	[-27:90:1]	Generators of the group modulo torsion
j	35242105/19683	j-invariant
L	4.0036644743155	L(r)(E,1)/r!
Ω	0.99120922729975	Real period
R	0.14959895987152	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	65025bz1 21675m1 21675e1	Quadratic twists by: -3 5 17

Hecke Eigenvalues for elliptic curve 21675t1

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	-4	1	-	0	-3	0	2	-5	-2	-4	9	10	-7	13	-2	1	-13	4	5	-6	7

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Quadratic twists for elliptic curve 21675t1

-3	5	17
65025bz1	21675m1	21675e1

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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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