Cremona's table of elliptic curves

100800 = 2⁶ · 3² · 5² · 7

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 7+	Signs for the Atkin-Lehner involutions
Class	100800ki	Isogeny class
Conductor	100800	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	614400	Modular degree for the optimal curve
Δ	1185408000000000 = 216 · 33 · 59 · 73	Discriminant
Eigenvalues	2- 3+ 5- 7+ -2  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-175500,28250000]	[a1,a2,a3,a4,a6]
Generators	[125:2875:1]	Generators of the group modulo torsion
j	172974204/343	j-invariant
L	6.025696316199	L(r)(E,1)/r!
Ω	0.48747070753748	Real period
R	3.0902863636557	Regulator
r	1	Rank of the group of rational points
S	0.99999999924662	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	100800ck1 25200o1 100800kh1 100800kq1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 100800ki1

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	6	-4	4	-10	-6	-10	-2	-6	6	2	-12	4	14	-4	2	8	4	6	-2

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Quadratic twists for elliptic curve 100800ki1

-4	8	-3	5
100800ck1	25200o1	100800kh1	100800kq1

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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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