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	3542g	Isogeny class
Conductor	3542	Conductor
∏ cp	96	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	-155579103523228 = -1 · 22 · 73 · 118 · 232	Discriminant
Eigenvalues	2+  2  0 7- 11-  0 -2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-5980,-628452]	[a1,a2,a3,a4,a6]
Generators	[207:2553:1]	Generators of the group modulo torsion
j	-23655968592999625/155579103523228	j-invariant
L	3.6532231833172	L(r)(E,1)/r!
Ω	0.24167089606499	Real period
R	0.62985504302216	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	28336s1 113344bc1 31878bk1 88550br1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3542g1

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

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Quadratic twists for elliptic curve 3542g1

-4	8	-3	5	-7	-11	-23
28336s1	113344bc1	31878bk1	88550br1	24794q1	38962v1	81466g1

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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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