Cremona's table of elliptic curves

3312 = 2⁴ · 3² · 23

Field	Data	Notes
Atkin-Lehner	2- 3+ 23+	Signs for the Atkin-Lehner involutions
Class	3312j	Isogeny class
Conductor	3312	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	2665550592 = 28 · 39 · 232	Discriminant
Eigenvalues	2- 3+ -2 -2  4 -2 -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-351,-486]	[a1,a2,a3,a4,a6]
j	949104/529	j-invariant
L	1.1836242837016	L(r)(E,1)/r!
Ω	1.1836242837016	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	828b2 13248y2 3312k2 82800co2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3312j2

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
-	+	-2	-2	4	-2	-2	2	+	-4	0	2	0	2	12	2	12	-14	-2	0	6	-6	4	18	6

---

Quadratic twists for elliptic curve 3312j2

-4	8	-3	5	-23
828b2	13248y2	3312k2	82800co2	76176bl2

---

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