Cremona's table of elliptic curves

84 = 2² · 3 · 7

Field	Data	Notes
Atkin-Lehner	2- 3- 7-	Signs for the Atkin-Lehner involutions
Class	84a	Isogeny class
Conductor	84	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-5647152 = -1 · 24 · 3 · 76	Discriminant
Eigenvalues	2- 3-  0 7- -6  2  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-113,-516]	[a1,a2,a3,a4,a6]
j	-10061824000/352947	j-invariant
L	1.0951585545828	L(r)(E,1)/r!
Ω	0.7301057030552	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	336a3 1344d3 252a3 2100c3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 84a3

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

---

Quadratic twists for elliptic curve 84a3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37
336a3	1344d3	252a3	2100c3	588b3	10164p3	14196h3	24276a3	30324c3	44436j3	70644d3	80724j3	114996l3

---

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