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	100800fk	Isogeny class
Conductor	100800	Conductor
∏ cp	64	Product of Tamagawa factors cp
deg	1179648	Modular degree for the optimal curve
Δ	-1435488571125000000 = -1 · 26 · 314 · 59 · 74	Discriminant
Eigenvalues	2+ 3- 5+ 7-  4 -2 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-260175,77019500]	[a1,a2,a3,a4,a6]
Generators	[1060:31500:1]	Generators of the group modulo torsion
j	-2671731885376/1969120125	j-invariant
L	6.8764520355601	L(r)(E,1)/r!
Ω	0.24788012539951	Real period
R	1.7338148886095	Regulator
r	1	Rank of the group of rational points
S	1.000000000499	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	100800ee1 50400br2 33600bc1 20160ca1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 100800fk1

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	-8	0	-2	0	-6	-2	4	8	6	0	2	4	-4	2	4	12	-18	-6

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Quadratic twists for elliptic curve 100800fk1

-4	8	-3	5
100800ee1	50400br2	33600bc1	20160ca1

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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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