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	3542a	Isogeny class
Conductor	3542	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	5408	Modular degree for the optimal curve
Δ	118849798144 = 226 · 7 · 11 · 23	Discriminant
Eigenvalues	2+ -1  1 7+ 11- -3  2  1	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-12897,-568907]	[a1,a2,a3,a4,a6]
Generators	[-22386:15289:343]	Generators of the group modulo torsion
j	237269779307308441/118849798144	j-invariant
L	2.1736126902285	L(r)(E,1)/r!
Ω	0.44800829147453	Real period
R	2.4258621230809	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	28336bh1 113344j1 31878ba1 88550bv1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3542a1

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	+	-	-3	2	1	-	6	0	10	-3	6	-13	-6	0	0	13	-12	-11	-8	-9	9	-7

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Quadratic twists for elliptic curve 3542a1

-4	8	-3	5	-7	-11	-23
28336bh1	113344j1	31878ba1	88550bv1	24794u1	38962bh1	81466o1

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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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