Cremona's table of elliptic curves

657 = 3² · 73

Field	Data	Notes
Atkin-Lehner	3- 73-	Signs for the Atkin-Lehner involutions
Class	657c	Isogeny class
Conductor	657	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-850780179 = -1 · 37 · 733	Discriminant
Eigenvalues	0 3-  3 -4  0 -4 -3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-246,2043]	[a1,a2,a3,a4,a6]
Generators	[-7:58:1]	Generators of the group modulo torsion
j	-2258403328/1167051	j-invariant
L	1.9853109737942	L(r)(E,1)/r!
Ω	1.4732708731893	Real period
R	2.0213298958695	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	10512x2 42048bc2 219b2 16425e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 657c2

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	-	3	-4	0	-4	-3	-1	-6	6	-10	-7	0	2	3	-9	9	-1	-13	-12	-	11	-15	18	5

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Quadratic twists for elliptic curve 657c2

-4	8	-3	5	-7	-11	13	73
10512x2	42048bc2	219b2	16425e2	32193d2	79497f2	111033c2	47961a2

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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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