Cremona's table of elliptic curves

8184 = 2³ · 3 · 11 · 31

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11- 31-	Signs for the Atkin-Lehner involutions
Class	8184d	Isogeny class
Conductor	8184	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	-5363809968 = -1 · 24 · 3 · 112 · 314	Discriminant
Eigenvalues	2+ 3+ -2  0 11- -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-199,-3620]	[a1,a2,a3,a4,a6]
Generators	[3771:231539:1]	Generators of the group modulo torsion
j	-54744881152/335238123	j-invariant
L	3.017785238978	L(r)(E,1)/r!
Ω	0.56770671900699	Real period
R	5.3157469128719	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	16368j1 65472t1 24552o1 90024v1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 8184d1

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

---

Quadratic twists for elliptic curve 8184d1

-4	8	-3	-11
16368j1	65472t1	24552o1	90024v1

---

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