Cremona's table of elliptic curves

8528 = 2⁴ · 13 · 41

Field	Data	Notes
Atkin-Lehner	2- 13+ 41-	Signs for the Atkin-Lehner involutions
Class	8528g	Isogeny class
Conductor	8528	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	12585806331904 = 218 · 134 · 412	Discriminant
Eigenvalues	2-  0 -2  0  0 13+ -6  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-7771,200970]	[a1,a2,a3,a4,a6]
Generators	[2079:94710:1]	Generators of the group modulo torsion
j	12670521525297/3072706624	j-invariant
L	3.405829193528	L(r)(E,1)/r!
Ω	0.66768686118668	Real period
R	5.1009378670037	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1066e2 34112t2 76752bq2 110864e2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 8528g2

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	8	0	10	0	6	-	4	8	-6	12	-10	-8	-8	10	-8	12	2	18

---

Quadratic twists for elliptic curve 8528g2

-4	8	-3	13
1066e2	34112t2	76752bq2	110864e2

---

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