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	100800jp	Isogeny class
Conductor	100800	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	221184	Modular degree for the optimal curve
Δ	44089920000000 = 212 · 39 · 57 · 7	Discriminant
Eigenvalues	2- 3+ 5+ 7-  0 -2  4  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-29700,-1944000]	[a1,a2,a3,a4,a6]
Generators	[2410:118000:1]	Generators of the group modulo torsion
j	2299968/35	j-invariant
L	7.5401892341576	L(r)(E,1)/r!
Ω	0.36400793724925	Real period
R	5.1785884844227	Regulator
r	1	Rank of the group of rational points
S	0.99999999812311	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	100800ip1 50400g1 100800jq1 20160cq1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 100800jp1

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

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Quadratic twists for elliptic curve 100800jp1

-4	8	-3	5
100800ip1	50400g1	100800jq1	20160cq1

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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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