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	3542n	Isogeny class
Conductor	3542	Conductor
∏ cp	70	Product of Tamagawa factors cp
deg	3360	Modular degree for the optimal curve
Δ	69667569664 = 214 · 75 · 11 · 23	Discriminant
Eigenvalues	2-  1 -3 7- 11+  1  2 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2547,-48031]	[a1,a2,a3,a4,a6]
Generators	[-26:41:1]	Generators of the group modulo torsion
j	1827347754908593/69667569664	j-invariant
L	5.0717582235752	L(r)(E,1)/r!
Ω	0.67361191753219	Real period
R	0.10755998672597	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	28336bc1 113344bq1 31878w1 88550c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3542n1

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	-3	-	+	1	2	-1	+	2	-8	-6	1	-10	-3	2	0	4	-9	-12	9	-4	1	-3	-19

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Quadratic twists for elliptic curve 3542n1

-4	8	-3	5	-7	-11	-23
28336bc1	113344bq1	31878w1	88550c1	24794be1	38962d1	81466bd1

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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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