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	100800mf	Isogeny class
Conductor	100800	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	514382400000000 = 212 · 38 · 58 · 72	Discriminant
Eigenvalues	2- 3- 5+ 7+ -4  6 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-63300,6032000]	[a1,a2,a3,a4,a6]
Generators	[-20:2700:1]	Generators of the group modulo torsion
j	601211584/11025	j-invariant
L	6.563837541904	L(r)(E,1)/r!
Ω	0.52238300125556	Real period
R	1.5706477588232	Regulator
r	1	Rank of the group of rational points
S	1.0000000031306	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	100800nt2 50400dg1 33600en2 20160fj2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 100800mf2

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

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Quadratic twists for elliptic curve 100800mf2

-4	8	-3	5
100800nt2	50400dg1	33600en2	20160fj2

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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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