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	21675c	Isogeny class
Conductor	21675	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	61861949300390625 = 38 · 58 · 176	Discriminant
Eigenvalues	1 3+ 5+  0  4  2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-975525,-371070000]	[a1,a2,a3,a4,a6]
Generators	[-4079087811930:-968004770853:7189057000]	Generators of the group modulo torsion
j	272223782641/164025	j-invariant
L	5.5245632085881	L(r)(E,1)/r!
Ω	0.15191672959771	Real period
R	18.182866440114	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	65025bn6 4335d5 75b5	Quadratic twists by: -3 5 17

Hecke Eigenvalues for elliptic curve 21675c6

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

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Quadratic twists for elliptic curve 21675c6

-3	5	17
65025bn6	4335d5	75b5

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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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