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	100800gm	Isogeny class
Conductor	100800	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	803538792000000000 = 212 · 315 · 59 · 7	Discriminant
Eigenvalues	2+ 3- 5- 7+  2  2  0 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-826684500,9148666700000]	[a1,a2,a3,a4,a6]
Generators	[-33086:530712:1]	Generators of the group modulo torsion
j	10713357105862263488/137781	j-invariant
L	7.1130581755274	L(r)(E,1)/r!
Ω	0.14332623462266	Real period
R	6.203555629402	Regulator
r	1	Rank of the group of rational points
S	1.0000000025942	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	100800hs2 50400ea1 33600bi2 100800hq2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 100800gm2

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

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Quadratic twists for elliptic curve 100800gm2

-4	8	-3	5
100800hs2	50400ea1	33600bi2	100800hq2

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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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