Cremona's table of elliptic curves

3332 = 2² · 7² · 17

Field	Data	Notes
Atkin-Lehner	2- 7+ 17+	Signs for the Atkin-Lehner involutions
Class	3332b	Isogeny class
Conductor	3332	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	2016	Modular degree for the optimal curve
Δ	-25088413952 = -1 · 28 · 78 · 17	Discriminant
Eigenvalues	2- -1  0 7+ -5 -5 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,572,-5704]	[a1,a2,a3,a4,a6]
j	14000/17	j-invariant
L	0.64030127442943	L(r)(E,1)/r!
Ω	0.64030127442943	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13328g1 53312a1 29988u1 83300b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3332b1

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	0	+	-5	-5	+	-6	4	4	0	8	4	-6	-6	11	10	0	10	9	4	9	4	-15	-18

---

Quadratic twists for elliptic curve 3332b1

-4	8	-3	5	-7	17
13328g1	53312a1	29988u1	83300b1	3332d1	56644a1

---

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