Cremona's table of elliptic curves

198 = 2 · 3² · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 11-	Signs for the Atkin-Lehner involutions
Class	198b	Isogeny class
Conductor	198	Conductor
∏ cp	36	Product of Tamagawa factors cp
Δ	186297408 = 26 · 37 · 113	Discriminant
Eigenvalues	2- 3-  0  2 11- -4  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-725,7661]	[a1,a2,a3,a4,a6]
j	57736239625/255552	j-invariant
L	1.8053975905613	L(r)(E,1)/r!
Ω	1.8053975905613	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	1584l3 6336k3 66a3 4950o3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 198b3

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

---

Quadratic twists for elliptic curve 198b3

-4	8	-3	5	-7	-11	13	17	-19	-23
1584l3	6336k3	66a3	4950o3	9702ca3	2178c3	33462q3	57222bh3	71478ba3	104742bl3

---

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