Cremona's table of elliptic curves

33856 = 2⁶ · 23²

Field	Data	Notes
Atkin-Lehner	2+ 23-	Signs for the Atkin-Lehner involutions
Class	33856o	Isogeny class
Conductor	33856	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	-33856 = -1 · 26 · 232	Discriminant
Eigenvalues	2+  2 -3 -4  2 -5 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,8,-6]	[a1,a2,a3,a4,a6]
Generators	[3:6:1] [42:99:8]	Generators of the group modulo torsion
j	1472	j-invariant
L	9.0858000585937	L(r)(E,1)/r!
Ω	2.0879954734853	Real period
R	4.3514462430451	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	33856s1 16928f1 33856m1	Quadratic twists by: -4 8 -23

Hecke Eigenvalues for elliptic curve 33856o1

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	-3	-4	2	-5	-6	4	-	3	-6	-6	3	2	6	-11	-8	-15	-16	-8	-13	4	-6	-11	-7

---

Quadratic twists for elliptic curve 33856o1

-4	8	-23
33856s1	16928f1	33856m1

---

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