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	1596a	Isogeny class
Conductor	1596	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	1344	Modular degree for the optimal curve
Δ	-223449429168 = -1 · 24 · 37 · 72 · 194	Discriminant
Eigenvalues	2- 3+  0 7+  2  2  0 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-113,-22710]	[a1,a2,a3,a4,a6]
j	-10061824000/13965589323	j-invariant
L	1.3490013482077	L(r)(E,1)/r!
Ω	0.44966711606923	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6384bf1 25536bh1 4788a1 39900r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1596a1

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	2	0	+	2	-6	8	-6	0	12	8	14	8	-2	0	-6	-2	4	16	16	-2

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Quadratic twists for elliptic curve 1596a1

-4	8	-3	5	-7	-19
6384bf1	25536bh1	4788a1	39900r1	11172s1	30324g1

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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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