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	100800ek	Isogeny class
Conductor	100800	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	-725896442880000000 = -1 · 216 · 310 · 57 · 74	Discriminant
Eigenvalues	2+ 3- 5+ 7-  0  2  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-36300,41078000]	[a1,a2,a3,a4,a6]
Generators	[40:6300:1]	Generators of the group modulo torsion
j	-7086244/972405	j-invariant
L	7.7622244328453	L(r)(E,1)/r!
Ω	0.23361541975252	Real period
R	1.0383283511149	Regulator
r	1	Rank of the group of rational points
S	0.9999999997517	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	100800kx3 12600r4 33600o3 20160bx4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 100800ek3

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

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Quadratic twists for elliptic curve 100800ek3

-4	8	-3	5
100800kx3	12600r4	33600o3	20160bx4

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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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