Cremona's table of elliptic curves

3192 = 2³ · 3 · 7 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7- 19-	Signs for the Atkin-Lehner involutions
Class	3192d	Isogeny class
Conductor	3192	Conductor
∏ cp	40	Product of Tamagawa factors cp
Δ	366868062231552 = 210 · 310 · 75 · 192	Discriminant
Eigenvalues	2+ 3+  0 7-  2 -4  0 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-360088,83283964]	[a1,a2,a3,a4,a6]
Generators	[106:6804:1]	Generators of the group modulo torsion
j	5042558062190438500/358269592023	j-invariant
L	3.0164726048303	L(r)(E,1)/r!
Ω	0.51055778597355	Real period
R	0.5908190390395	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	6384g2 25536bn2 9576ba2 79800bo2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3192d2

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	-4	0	-	-6	2	4	2	2	-8	-8	-6	-4	14	-2	0	-6	-10	0	18	-16

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Quadratic twists for elliptic curve 3192d2

-4	8	-3	5	-7	-19
6384g2	25536bn2	9576ba2	79800bo2	22344q2	60648bn2

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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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