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	3542c	Isogeny class
Conductor	3542	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	1728	Modular degree for the optimal curve
Δ	-87820348 = -1 · 22 · 73 · 112 · 232	Discriminant
Eigenvalues	2+ -2 -2 7- 11+ -6 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-162,896]	[a1,a2,a3,a4,a6]
Generators	[-13:35:1] [-4:40:1]	Generators of the group modulo torsion
j	-466025146777/87820348	j-invariant
L	2.346756982607	L(r)(E,1)/r!
Ω	1.8361122912884	Real period
R	0.213018651214	Regulator
r	2	Rank of the group of rational points
S	1.0000000000003	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	28336bf1 113344bu1 31878br1 88550bj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3542c1

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

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Quadratic twists for elliptic curve 3542c1

-4	8	-3	5	-7	-11	-23
28336bf1	113344bu1	31878br1	88550bj1	24794c1	38962z1	81466m1

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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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