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	100800hk	Isogeny class
Conductor	100800	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	-3584673792000 = -1 · 214 · 36 · 53 · 74	Discriminant
Eigenvalues	2+ 3- 5- 7-  0 -4 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1980,97200]	[a1,a2,a3,a4,a6]
Generators	[10:-280:1] [-30:360:1]	Generators of the group modulo torsion
j	-574992/2401	j-invariant
L	11.737265331548	L(r)(E,1)/r!
Ω	0.68804357279478	Real period
R	0.53309057176509	Regulator
r	2	Rank of the group of rational points
S	0.99999999997387	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	100800oi2 6300z2 11200bl2 100800gd2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 100800hk2

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

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Quadratic twists for elliptic curve 100800hk2

-4	8	-3	5
100800oi2	6300z2	11200bl2	100800gd2

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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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