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	100800pw	Isogeny class
Conductor	100800	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	3429216000000000 = 214 · 37 · 59 · 72	Discriminant
Eigenvalues	2- 3- 5- 7- -4  2  2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-61500,-5150000]	[a1,a2,a3,a4,a6]
Generators	[-114:616:1]	Generators of the group modulo torsion
j	1102736/147	j-invariant
L	6.9418948344072	L(r)(E,1)/r!
Ω	0.30583796558365	Real period
R	2.837243746666	Regulator
r	1	Rank of the group of rational points
S	0.99999999879644	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	100800gz2 25200fs2 33600hm2 100800pa2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 100800pw2

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

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Quadratic twists for elliptic curve 100800pw2

-4	8	-3	5
100800gz2	25200fs2	33600hm2	100800pa2

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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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