Cremona's table of elliptic curves

10032 = 2⁴ · 3 · 11 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 11+ 19-	Signs for the Atkin-Lehner involutions
Class	10032o	Isogeny class
Conductor	10032	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	3117456359424 = 216 · 32 · 114 · 192	Discriminant
Eigenvalues	2- 3- -2  0 11+ -2 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3664,7316]	[a1,a2,a3,a4,a6]
j	1328460616657/761097744	j-invariant
L	1.3668281160702	L(r)(E,1)/r!
Ω	0.68341405803512	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1254h2 40128bm2 30096bk2 110352bz2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 10032o2

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	0	+	-2	-6	-	0	-2	0	-2	-6	-4	8	6	12	-2	4	16	10	0	12	10	2

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Quadratic twists for elliptic curve 10032o2

-4	8	-3	-11
1254h2	40128bm2	30096bk2	110352bz2

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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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