Cremona's table of elliptic curves

6600 = 2³ · 3 · 5² · 11

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 11+	Signs for the Atkin-Lehner involutions
Class	6600a	Isogeny class
Conductor	6600	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	618750000000000 = 210 · 32 · 514 · 11	Discriminant
Eigenvalues	2+ 3+ 5+  0 11+  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-58008,5262012]	[a1,a2,a3,a4,a6]
Generators	[162:300:1]	Generators of the group modulo torsion
j	1349195526724/38671875	j-invariant
L	3.4490294953967	L(r)(E,1)/r!
Ω	0.5119561216908	Real period
R	1.6842407724347	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	13200u3 52800cq3 19800bh3 1320m4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6600a4

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

---

Quadratic twists for elliptic curve 6600a4

-4	8	-3	5	-11
13200u3	52800cq3	19800bh3	1320m4	72600ck3

---

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