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	100800gn	Isogeny class
Conductor	100800	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	589824	Modular degree for the optimal curve
Δ	13826598912000 = 214 · 39 · 53 · 73	Discriminant
Eigenvalues	2+ 3- 5- 7+  2 -2  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-555420,159323600]	[a1,a2,a3,a4,a6]
Generators	[406:864:1]	Generators of the group modulo torsion
j	12692020761488/9261	j-invariant
L	5.815142779799	L(r)(E,1)/r!
Ω	0.58556833973725	Real period
R	1.2413458836584	Regulator
r	1	Rank of the group of rational points
S	0.99999999909393	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	100800po1 12600ba1 33600bj1 100800ho1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 100800gn1

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

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Quadratic twists for elliptic curve 100800gn1

-4	8	-3	5
100800po1	12600ba1	33600bj1	100800ho1

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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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