Cremona's table of elliptic curves

3658 = 2 · 31 · 59

Field	Data	Notes
Atkin-Lehner	2- 31- 59+	Signs for the Atkin-Lehner involutions
Class	3658d	Isogeny class
Conductor	3658	Conductor
∏ cp	54	Product of Tamagawa factors cp
Δ	-93324604672050688 = -1 · 29 · 316 · 593	Discriminant
Eigenvalues	2- -2  0 -1 -3  5 -3  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,49377,14082265]	[a1,a2,a3,a4,a6]
Generators	[-172:799:1]	Generators of the group modulo torsion
j	13313653880668607375/93324604672050688	j-invariant
L	3.6219068044219	L(r)(E,1)/r!
Ω	0.24608551709136	Real period
R	2.453013656412	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	29264f2 117056i2 32922c2 91450e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3658d2

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
-	-2	0	-1	-3	5	-3	2	6	-6	-	-7	9	-1	-6	12	+	-10	-4	3	2	-1	-3	-18	-10

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Quadratic twists for elliptic curve 3658d2

-4	8	-3	5	-31
29264f2	117056i2	32922c2	91450e2	113398f2

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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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