Cremona's table of elliptic curves

427 = 7 · 61

Field	Data	Notes
Atkin-Lehner	7- 61-	Signs for the Atkin-Lehner involutions
Class	427b	Isogeny class
Conductor	427	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	28	Modular degree for the optimal curve
Δ	427 = 7 · 61	Discriminant
Eigenvalues	1  1 -4 7- -3 -4  5  1	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-8,7]	[a1,a2,a3,a4,a6]
Generators	[1:0:1]	Generators of the group modulo torsion
j	47045881/427	j-invariant
L	2.161700267695	L(r)(E,1)/r!
Ω	5.3267648633371	Real period
R	0.40581860156311	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	6832g1 27328g1 3843j1 10675d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 427b1

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	1	-4	-	-3	-4	5	1	7	-10	-8	10	-6	-1	-9	-2	-6	-	3	-1	-2	-5	-15	5	14

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Quadratic twists for elliptic curve 427b1

-4	8	-3	5	-7	-11	13	17	61
6832g1	27328g1	3843j1	10675d1	2989a1	51667c1	72163c1	123403a1	26047b1

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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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