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	1596d	Isogeny class
Conductor	1596	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-41604528 = -1 · 24 · 3 · 74 · 192	Discriminant
Eigenvalues	2- 3- -2 7+ -2  2  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-309,-2220]	[a1,a2,a3,a4,a6]
j	-204589760512/2600283	j-invariant
L	1.7063007427816	L(r)(E,1)/r!
Ω	0.56876691426053	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	6384w1 25536a1 4788c1 39900i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1596d1

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	+	-2	2	2	-	6	0	8	6	0	8	-6	0	0	10	4	8	6	-8	6	-8	6

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Quadratic twists for elliptic curve 1596d1

-4	8	-3	5	-7	-19
6384w1	25536a1	4788c1	39900i1	11172c1	30324b1

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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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