Cremona's table of elliptic curves

8820 = 2² · 3² · 5 · 7²

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 7-	Signs for the Atkin-Lehner involutions
Class	8820z	Isogeny class
Conductor	8820	Conductor
∏ cp	192	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	42195431250000 = 24 · 39 · 58 · 73	Discriminant
Eigenvalues	2- 3- 5- 7- -2  4  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-13692,531601]	[a1,a2,a3,a4,a6]
Generators	[-28:945:1]	Generators of the group modulo torsion
j	70954958848/10546875	j-invariant
L	4.7368208559582	L(r)(E,1)/r!
Ω	0.61656504548614	Real period
R	0.16005410711315	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	35280fk1 2940g1 44100bx1 8820m1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8820z1

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

---

Quadratic twists for elliptic curve 8820z1

-4	-3	5	-7
35280fk1	2940g1	44100bx1	8820m1

---

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