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	100800mg	Isogeny class
Conductor	100800	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	589824	Modular degree for the optimal curve
Δ	-8360755200000000 = -1 · 222 · 36 · 58 · 7	Discriminant
Eigenvalues	2- 3- 5+ 7+ -4 -6  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,33300,-3726000]	[a1,a2,a3,a4,a6]
Generators	[4770:120825:8]	Generators of the group modulo torsion
j	1367631/2800	j-invariant
L	4.516833438322	L(r)(E,1)/r!
Ω	0.21549310511034	Real period
R	5.24011363738	Regulator
r	1	Rank of the group of rational points
S	1.0000000006469	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	100800fn1 25200dy1 11200bu1 20160ei1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 100800mg1

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
-	-	+	+	-4	-6	2	0	0	6	-8	-10	-2	-4	-8	2	8	14	12	-16	-2	8	8	-10	-2

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Quadratic twists for elliptic curve 100800mg1

-4	8	-3	5
100800fn1	25200dy1	11200bu1	20160ei1

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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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