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	8	Product of Tamagawa factors cp
Δ	-128608722 = -1 · 2 · 312 · 112	Discriminant
Eigenvalues	2- 3-  0  2 11- -4  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,40,-547]	[a1,a2,a3,a4,a6]
j	9938375/176418	j-invariant
L	1.8053975905613	L(r)(E,1)/r!
Ω	0.90269879528067	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	1584l2 6336k2 66a2 4950o2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 198b2

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 198b2

-4	8	-3	5	-7	-11	13	17	-19	-23
1584l2	6336k2	66a2	4950o2	9702ca2	2178c2	33462q2	57222bh2	71478ba2	104742bl2

---

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