Cremona's table of elliptic curves

3538 = 2 · 29 · 61

Field	Data	Notes
Atkin-Lehner	2+ 29+ 61+	Signs for the Atkin-Lehner involutions
Class	3538a	Isogeny class
Conductor	3538	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	12517444 = 22 · 292 · 612	Discriminant
Eigenvalues	2+  0 -2 -4  4 -2  6  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-58,0]	[a1,a2,a3,a4,a6]
Generators	[-1:8:1]	Generators of the group modulo torsion
j	21787771257/12517444	j-invariant
L	1.9583991816258	L(r)(E,1)/r!
Ω	1.8783357618286	Real period
R	2.0852493163621	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	28304a2 113216f2 31842bb2 88450k2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3538a2

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	4	-2	6	8	-4	+	0	-6	10	4	0	2	4	+	4	12	-14	0	-12	-18	-6

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Quadratic twists for elliptic curve 3538a2

-4	8	-3	5	29
28304a2	113216f2	31842bb2	88450k2	102602c2

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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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