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	100800gz	Isogeny class
Conductor	100800	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	245760	Modular degree for the optimal curve
Δ	-91854000000000 = -1 · 210 · 38 · 59 · 7	Discriminant
Eigenvalues	2+ 3- 5- 7+  4  2  2  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,6000,425000]	[a1,a2,a3,a4,a6]
Generators	[5950:459000:1]	Generators of the group modulo torsion
j	16384/63	j-invariant
L	7.7118148803419	L(r)(E,1)/r!
Ω	0.42902758053279	Real period
R	4.4937757108325	Regulator
r	1	Rank of the group of rational points
S	0.99999999969397	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	100800pw1 6300x1 33600br1 100800ih1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 100800gz1

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

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Quadratic twists for elliptic curve 100800gz1

-4	8	-3	5
100800pw1	6300x1	33600br1	100800ih1

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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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