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	3542o	Isogeny class
Conductor	3542	Conductor
∏ cp	288	Product of Tamagawa factors cp
deg	13824	Modular degree for the optimal curve
Δ	-368345236897792 = -1 · 224 · 73 · 112 · 232	Discriminant
Eigenvalues	2- -2  0 7- 11+  2  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-30538,2249508]	[a1,a2,a3,a4,a6]
Generators	[-158:1850:1]	Generators of the group modulo torsion
j	-3149534523783390625/368345236897792	j-invariant
L	3.7947525505348	L(r)(E,1)/r!
Ω	0.52163893393192	Real period
R	0.90933409675044	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	28336bd1 113344bs1 31878r1 88550g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3542o1

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	-	+	2	0	-4	+	-6	2	2	-6	-4	6	6	-6	8	-4	0	-10	-16	0	12	8

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Quadratic twists for elliptic curve 3542o1

-4	8	-3	5	-7	-11	-23
28336bd1	113344bs1	31878r1	88550g1	24794bg1	38962f1	81466be1

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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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