Cremona's table of elliptic curves

82656 = 2⁵ · 3² · 7 · 41

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 41+	Signs for the Atkin-Lehner involutions
Class	82656u	Isogeny class
Conductor	82656	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	22148902476288 = 29 · 37 · 7 · 414	Discriminant
Eigenvalues	2+ 3-  2 7-  4 -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-7059,-28982]	[a1,a2,a3,a4,a6]
Generators	[4786908710:-51474147939:29791000]	Generators of the group modulo torsion
j	104221127816/59340981	j-invariant
L	8.8224480595658	L(r)(E,1)/r!
Ω	0.56312785965165	Real period
R	15.666864826399	Regulator
r	1	Rank of the group of rational points
S	1.0000000002748	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	82656i3 27552bc3	Quadratic twists by: -4 -3

Hecke Eigenvalues for elliptic curve 82656u3

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	-	4	-2	6	-4	-4	-6	4	6	+	0	-8	-6	0	-2	4	0	10	-8	0	-18	-10

---

Quadratic twists for elliptic curve 82656u3

-4	-3
82656i3	27552bc3

---

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