Cremona's table of elliptic curves

3362 = 2 · 41²

Field	Data	Notes
Atkin-Lehner	2+ 41+	Signs for the Atkin-Lehner involutions
Class	3362c	Isogeny class
Conductor	3362	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	1102736 = 24 · 413	Discriminant
Eigenvalues	2+ -2  2  2  6 -4  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-3500,-79974]	[a1,a2,a3,a4,a6]
Generators	[222:3066:1]	Generators of the group modulo torsion
j	68769820673/16	j-invariant
L	2.2900427422139	L(r)(E,1)/r!
Ω	0.62072239552607	Real period
R	3.689318701435	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	26896c2 107584c2 30258t2 84050k2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3362c2

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

---

Quadratic twists for elliptic curve 3362c2

-4	8	-3	5	41
26896c2	107584c2	30258t2	84050k2	3362a2

---

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