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	3192c	Isogeny class
Conductor	3192	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	3707605343232 = 210 · 34 · 73 · 194	Discriminant
Eigenvalues	2+ 3+ -2 7+ -4  2 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-592824,175883580]	[a1,a2,a3,a4,a6]
j	22501000029889239268/3620708343	j-invariant
L	0.61750109449595	L(r)(E,1)/r!
Ω	0.61750109449595	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	6384n3 25536bb4 9576v3 79800bu4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3192c3

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	+	-4	2	-6	-	0	-10	8	-2	6	4	-8	6	-4	-10	8	12	-14	-4	-4	6	14

---

Quadratic twists for elliptic curve 3192c3

-4	8	-3	5	-7	-19
6384n3	25536bb4	9576v3	79800bu4	22344t4	60648bk4

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations