Cremona's table of elliptic curves

4032 = 2⁶ · 3² · 7

Field	Data	Notes
Atkin-Lehner	2+ 3- 7-	Signs for the Atkin-Lehner involutions
Class	4032n	Isogeny class
Conductor	4032	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	36870930432 = 214 · 38 · 73	Discriminant
Eigenvalues	2+ 3-  0 7- -6 -2  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-65820,6499568]	[a1,a2,a3,a4,a6]
Generators	[136:252:1]	Generators of the group modulo torsion
j	2640279346000/3087	j-invariant
L	3.5648217300693	L(r)(E,1)/r!
Ω	0.97566368032908	Real period
R	0.60895672042559	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	4032bb4 252a4 1344d4 100800ej4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4032n4

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

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Quadratic twists for elliptic curve 4032n4

-4	8	-3	5	-7
4032bb4	252a4	1344d4	100800ej4	28224bo4

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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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