Cremona's table of elliptic curves

3300 = 2² · 3 · 5² · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 11+	Signs for the Atkin-Lehner involutions
Class	3300k	Isogeny class
Conductor	3300	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	36300000000 = 28 · 3 · 58 · 112	Discriminant
Eigenvalues	2- 3- 5+  2 11+ -2 -8 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-9908,-382812]	[a1,a2,a3,a4,a6]
Generators	[168:1650:1]	Generators of the group modulo torsion
j	26894628304/9075	j-invariant
L	4.1431233466259	L(r)(E,1)/r!
Ω	0.47852892816748	Real period
R	2.8860138525599	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13200bs2 52800bb2 9900p2 660a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3300k2

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	-8	-2	-8	0	0	-2	0	-6	-8	-6	-4	10	12	8	-10	-14	-4	10	18

---

Quadratic twists for elliptic curve 3300k2

-4	8	-3	5	-11
13200bs2	52800bb2	9900p2	660a2	36300bo2

---

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