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	10032i	Isogeny class
Conductor	10032	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-74406726991872 = -1 · 219 · 32 · 112 · 194	Discriminant
Eigenvalues	2- 3+  0  2 11- -4  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,6952,-352272]	[a1,a2,a3,a4,a6]
Generators	[44:192:1]	Generators of the group modulo torsion
j	9070486526375/18165704832	j-invariant
L	4.0035463337835	L(r)(E,1)/r!
Ω	0.31972580390116	Real period
R	1.5652264709846	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	1254d2 40128bu2 30096s2 110352bi2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 10032i2

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

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Quadratic twists for elliptic curve 10032i2

-4	8	-3	-11
1254d2	40128bu2	30096s2	110352bi2

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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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