Cremona's table of elliptic curves

10332 = 2² · 3² · 7 · 41

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 41+	Signs for the Atkin-Lehner involutions
Class	10332d	Isogeny class
Conductor	10332	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	-496029235968 = -1 · 28 · 39 · 74 · 41	Discriminant
Eigenvalues	2- 3- -2 7+  3 -4 -1  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1776,-44476]	[a1,a2,a3,a4,a6]
Generators	[100:882:1]	Generators of the group modulo torsion
j	-3319595008/2657907	j-invariant
L	3.727115988702	L(r)(E,1)/r!
Ω	0.35553298711497	Real period
R	0.87359826040014	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	41328cb1 3444b1 72324r1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 10332d1

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	+	3	-4	-1	6	-4	5	5	-11	+	1	9	-6	4	-3	14	15	-7	-14	-10	10	-10

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Quadratic twists for elliptic curve 10332d1

-4	-3	-7
41328cb1	3444b1	72324r1

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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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