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	100800gt	Isogeny class
Conductor	100800	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-276468770930688000 = -1 · 220 · 316 · 53 · 72	Discriminant
Eigenvalues	2+ 3- 5- 7+ -2  2  8  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-40620,-25493200]	[a1,a2,a3,a4,a6]
Generators	[42340:985635:64]	Generators of the group modulo torsion
j	-310288733/11573604	j-invariant
L	7.1881978936291	L(r)(E,1)/r!
Ω	0.13489065993736	Real period
R	6.661133824084	Regulator
r	1	Rank of the group of rational points
S	0.99999999915623	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	100800pl2 3150bo2 33600bf2 100800ht2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 100800gt2

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

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Quadratic twists for elliptic curve 100800gt2

-4	8	-3	5
100800pl2	3150bo2	33600bf2	100800ht2

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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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