Cremona's table of elliptic curves

427 = 7 · 61

Field	Data	Notes
Atkin-Lehner	7- 61+	Signs for the Atkin-Lehner involutions
Class	427a	Isogeny class
Conductor	427	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	22	Modular degree for the optimal curve
Δ	-427 = -1 · 7 · 61	Discriminant
Eigenvalues	0  2  4 7- -2  2  5 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-1,-1]	[a1,a2,a3,a4,a6]
j	-262144/427	j-invariant
L	2.1028874776884	L(r)(E,1)/r!
Ω	2.1028874776884	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	6832d1 27328m1 3843h1 10675a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 427a1

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	2	4	-	-2	2	5	-8	-6	2	1	4	0	8	-8	-12	1	+	6	6	-10	-14	-2	10	-2

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Quadratic twists for elliptic curve 427a1

-4	8	-3	5	-7	-11	13	17	61
6832d1	27328m1	3843h1	10675a1	2989b1	51667f1	72163a1	123403c1	26047a1

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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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