Cremona's table of elliptic curves

2828 = 2² · 7 · 101

Field	Data	Notes
Atkin-Lehner	2- 7+ 101+	Signs for the Atkin-Lehner involutions
Class	2828a	Isogeny class
Conductor	2828	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	420	Modular degree for the optimal curve
Δ	-27160112 = -1 · 24 · 75 · 101	Discriminant
Eigenvalues	2- -1  0 7+ -2  4 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,27,-254]	[a1,a2,a3,a4,a6]
j	131072000/1697507	j-invariant
L	1.0344873313295	L(r)(E,1)/r!
Ω	1.0344873313295	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	11312j1 45248e1 25452b1 70700d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2828a1

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
-	-1	0	+	-2	4	-2	0	-1	-6	10	7	-6	-9	4	2	9	7	10	-1	-7	13	-13	1	-10

---

Quadratic twists for elliptic curve 2828a1

-4	8	-3	5	-7
11312j1	45248e1	25452b1	70700d1	19796b1

---

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