Cremona's table of elliptic curves

3542 = 2 · 7 · 11 · 23

Field	Data	Notes
Atkin-Lehner	2- 7- 11- 23-	Signs for the Atkin-Lehner involutions
Class	3542r	Isogeny class
Conductor	3542	Conductor
∏ cp	750	Product of Tamagawa factors cp
deg	36000	Modular degree for the optimal curve
Δ	147437307865222144 = 210 · 75 · 113 · 235	Discriminant
Eigenvalues	2- -1  1 7- 11- -1 -2 -5	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-258685,47043603]	[a1,a2,a3,a4,a6]
Generators	[-579:2060:1]	Generators of the group modulo torsion
j	1914421473306136725841/147437307865222144	j-invariant
L	4.5910737728699	L(r)(E,1)/r!
Ω	0.31862794191464	Real period
R	0.48029620851643	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	5	Number of elements in the torsion subgroup
Twists	28336l1 113344bi1 31878k1 88550i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3542r1

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	-	-	-1	-2	-5	-	-10	-8	-2	7	-6	3	-6	0	12	13	-8	-1	0	-11	-15	-7

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Quadratic twists for elliptic curve 3542r1

-4	8	-3	5	-7	-11	-23
28336l1	113344bi1	31878k1	88550i1	24794bs1	38962h1	81466y1

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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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