Cremona's table of elliptic curves

52256 = 2⁵ · 23 · 71

Field	Data	Notes
Atkin-Lehner	2- 23- 71+	Signs for the Atkin-Lehner involutions
Class	52256b	Isogeny class
Conductor	52256	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	312192	Modular degree for the optimal curve
Δ	-99750153885875648 = -1 · 26 · 233 · 716	Discriminant
Eigenvalues	2-  0 -2  0  0 -6 -4  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-103081,19828536]	[a1,a2,a3,a4,a6]
Generators	[449:8004:1]	Generators of the group modulo torsion
j	-1892690521713402048/1558596154466807	j-invariant
L	3.5952178786539	L(r)(E,1)/r!
Ω	0.30842029226787	Real period
R	3.8856261717882	Regulator
r	1	Rank of the group of rational points
S	1.0000000000039	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	52256a1 104512i2	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 52256b1

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

---

Quadratic twists for elliptic curve 52256b1

-4	8
52256a1	104512i2

---

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