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	3198d	Isogeny class
Conductor	3198	Conductor
∏ cp	140	Product of Tamagawa factors cp
deg	250880	Modular degree for the optimal curve
Δ	5899782742437003264 = 220 · 37 · 137 · 41	Discriminant
Eigenvalues	2- 3+  1  2 -5 13- -7  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-29960040,63106639209]	[a1,a2,a3,a4,a6]
Generators	[3069:7253:1]	Generators of the group modulo torsion
j	2974067900496992515620792961/5899782742437003264	j-invariant
L	4.5581016660811	L(r)(E,1)/r!
Ω	0.20579962117079	Real period
R	0.15820179288093	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	25584x1 102336v1 9594i1 79950p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3198d1

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
-	+	1	2	-5	-	-7	0	-9	-1	-5	4	+	6	-3	-9	-12	-1	8	8	8	-1	-4	10	17

---

Quadratic twists for elliptic curve 3198d1

-4	8	-3	5	13
25584x1	102336v1	9594i1	79950p1	41574c1

---

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