Cremona's table of elliptic curves

3333 = 3 · 11 · 101

Field	Data	Notes
Atkin-Lehner	3- 11- 101-	Signs for the Atkin-Lehner involutions
Class	3333f	Isogeny class
Conductor	3333	Conductor
∏ cp	60	Product of Tamagawa factors cp
Δ	-10565499454389 = -1 · 310 · 116 · 101	Discriminant
Eigenvalues	1 3-  2  4 11- -2 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-6200,-244969]	[a1,a2,a3,a4,a6]
j	-26351059610839033/10565499454389	j-invariant
L	3.9570493045422	L(r)(E,1)/r!
Ω	0.26380328696948	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	53328j2 9999g2 83325i2 36663i2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 3333f2

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	4	-	-2	-2	-2	6	6	8	2	10	-6	-10	4	4	4	4	-14	-4	14	-4	-16	-10

---

Quadratic twists for elliptic curve 3333f2

-4	-3	5	-11
53328j2	9999g2	83325i2	36663i2

---

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