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	10032h	Isogeny class
Conductor	10032	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	493092864 = 218 · 32 · 11 · 19	Discriminant
Eigenvalues	2- 3+ -2  2 11+ -2  6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-584,-5136]	[a1,a2,a3,a4,a6]
Generators	[-14:10:1]	Generators of the group modulo torsion
j	5386984777/120384	j-invariant
L	3.4169920807626	L(r)(E,1)/r!
Ω	0.9723556054229	Real period
R	1.7570691533559	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1254e1 40128ca1 30096bl1 110352ba1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 10032h1

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

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Quadratic twists for elliptic curve 10032h1

-4	8	-3	-11
1254e1	40128ca1	30096bl1	110352ba1

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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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