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	2828b	Isogeny class
Conductor	2828	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	636	Modular degree for the optimal curve
Δ	-11312 = -1 · 24 · 7 · 101	Discriminant
Eigenvalues	2- -3  0 7-  2 -4 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-160,-779]	[a1,a2,a3,a4,a6]
Generators	[15:14:1]	Generators of the group modulo torsion
j	-28311552000/707	j-invariant
L	2.0838263913391	L(r)(E,1)/r!
Ω	0.67117985450175	Real period
R	3.1047213013955	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	11312i1 45248r1 25452d1 70700b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2828b1

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
-	-3	0	-	2	-4	-2	0	-3	10	-2	3	10	1	-12	-6	-5	15	14	-11	-3	15	-15	5	-2

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Quadratic twists for elliptic curve 2828b1

-4	8	-3	5	-7
11312i1	45248r1	25452d1	70700b1	19796d1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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