Cremona's table of elliptic curves

7293 = 3 · 11 · 13 · 17

Field	Data	Notes
Atkin-Lehner	3- 11+ 13- 17+	Signs for the Atkin-Lehner involutions
Class	7293c	Isogeny class
Conductor	7293	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	3262914972603 = 33 · 114 · 134 · 172	Discriminant
Eigenvalues	-1 3-  2  0 11+ 13- 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-42042,-3320343]	[a1,a2,a3,a4,a6]
Generators	[-117:78:1]	Generators of the group modulo torsion
j	8218157522273610913/3262914972603	j-invariant
L	3.6643534848307	L(r)(E,1)/r!
Ω	0.33341797336188	Real period
R	0.91585581702017	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	116688s4 21879l4 80223n4 94809u4	Quadratic twists by: -4 -3 -11 13

Hecke Eigenvalues for elliptic curve 7293c3

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

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Quadratic twists for elliptic curve 7293c3

-4	-3	-11	13	17
116688s4	21879l4	80223n4	94809u4	123981i4

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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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