Cremona's table of elliptic curves

3393 = 3² · 13 · 29

Field	Data	Notes
Atkin-Lehner	3- 13- 29+	Signs for the Atkin-Lehner involutions
Class	3393g	Isogeny class
Conductor	3393	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-6702902037 = -1 · 36 · 13 · 294	Discriminant
Eigenvalues	-1 3-  2  0  4 13- -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,466,586]	[a1,a2,a3,a4,a6]
Generators	[5:52:1]	Generators of the group modulo torsion
j	15382515303/9194653	j-invariant
L	2.6137246175405	L(r)(E,1)/r!
Ω	0.81504875523282	Real period
R	3.2068322302926	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	54288bo3 377a4 84825m3 44109s3	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3393g4

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	0	4	-	-2	-4	-8	+	-8	2	10	-8	-8	-6	-12	6	12	16	-10	-12	12	10	14

---

Quadratic twists for elliptic curve 3393g4

-4	-3	5	13	29
54288bo3	377a4	84825m3	44109s3	98397x3

---

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