Cremona's table of elliptic curves

8010 = 2 · 3² · 5 · 89

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 89+	Signs for the Atkin-Lehner involutions
Class	8010h	Isogeny class
Conductor	8010	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	13824	Modular degree for the optimal curve
Δ	166095360000 = 212 · 36 · 54 · 89	Discriminant
Eigenvalues	2- 3- 5+  2  4 -2 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-10238,400781]	[a1,a2,a3,a4,a6]
Generators	[25:387:1]	Generators of the group modulo torsion
j	162780279643801/227840000	j-invariant
L	6.3865423482206	L(r)(E,1)/r!
Ω	1.0182125756769	Real period
R	0.52269228947395	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	64080r1 890e1 40050h1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 8010h1

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	-6	-2	2	-2	-2	-2	-10	-4	-2	6	-10	-12	12	-6	4	2	+	-2

---

Quadratic twists for elliptic curve 8010h1

-4	-3	5
64080r1	890e1	40050h1

---

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