Cremona's table of elliptic curves

3404 = 2² · 23 · 37

Field	Data	Notes
Atkin-Lehner	2- 23+ 37+	Signs for the Atkin-Lehner involutions
Class	3404a	Isogeny class
Conductor	3404	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	912	Modular degree for the optimal curve
Δ	5010688 = 28 · 232 · 37	Discriminant
Eigenvalues	2- -1  0 -5 -5 -4 -8  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-93,361]	[a1,a2,a3,a4,a6]
Generators	[-8:23:1] [-5:26:1]	Generators of the group modulo torsion
j	351232000/19573	j-invariant
L	3.3251648051694	L(r)(E,1)/r!
Ω	2.3922800867245	Real period
R	0.23165938523272	Regulator
r	2	Rank of the group of rational points
S	0.99999999999967	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13616g1 54464c1 30636c1 85100g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3404a1

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	0	-5	-5	-4	-8	6	+	0	-10	+	-5	6	-7	-1	10	-2	4	-13	-1	2	9	-4	-8

---

Quadratic twists for elliptic curve 3404a1

-4	8	-3	5	-23	37
13616g1	54464c1	30636c1	85100g1	78292g1	125948f1

---

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