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	2	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-1436859 = -1 · 39 · 73	Discriminant
Eigenvalues	0 3-  3 -4  0 -4 -3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,24,-36]	[a1,a2,a3,a4,a6]
Generators	[2:4:1]	Generators of the group modulo torsion
j	2097152/1971	j-invariant
L	1.9853109737942	L(r)(E,1)/r!
Ω	1.4732708731893	Real period
R	0.67377663195649	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	10512x1 42048bc1 219b1 16425e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 657c1

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 657c1

-4	8	-3	5	-7	-11	13	73
10512x1	42048bc1	219b1	16425e1	32193d1	79497f1	111033c1	47961a1

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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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