Cremona's table of elliptic curves

1596 = 2² · 3 · 7 · 19

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 19-	Signs for the Atkin-Lehner involutions
Class	1596b	Isogeny class
Conductor	1596	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	864	Modular degree for the optimal curve
Δ	-2038621872 = -1 · 24 · 3 · 76 · 192	Discriminant
Eigenvalues	2- 3+  0 7+ -2  6 -8 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,247,-1662]	[a1,a2,a3,a4,a6]
Generators	[7:19:1]	Generators of the group modulo torsion
j	103737344000/127413867	j-invariant
L	2.4208896360714	L(r)(E,1)/r!
Ω	0.78867580803857	Real period
R	1.0231874793151	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	6384bc1 25536x1 4788b1 39900u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1596b1

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

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Quadratic twists for elliptic curve 1596b1

-4	8	-3	5	-7	-19
6384bc1	25536x1	4788b1	39900u1	11172p1	30324h1

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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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