Cremona's table of elliptic curves

3198 = 2 · 3 · 13 · 41

Field	Data	Notes
Atkin-Lehner	2- 3- 13+ 41+	Signs for the Atkin-Lehner involutions
Class	3198f	Isogeny class
Conductor	3198	Conductor
∏ cp	70	Product of Tamagawa factors cp
deg	2240	Modular degree for the optimal curve
Δ	1193647104 = 210 · 37 · 13 · 41	Discriminant
Eigenvalues	2- 3- -3  0  1 13+ -3 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-802,8516]	[a1,a2,a3,a4,a6]
Generators	[-4:110:1]	Generators of the group modulo torsion
j	57053285789473/1193647104	j-invariant
L	4.9636645818592	L(r)(E,1)/r!
Ω	1.5381394481402	Real period
R	0.046100822725989	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	25584o1 102336p1 9594h1 79950f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3198f1

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
-	-	-3	0	1	+	-3	-4	-7	5	-1	-8	+	-8	9	1	6	1	-10	-8	8	-15	6	-16	11

---

Quadratic twists for elliptic curve 3198f1

-4	8	-3	5	13
25584o1	102336p1	9594h1	79950f1	41574i1

---

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