Cremona's table of elliptic curves

13294 = 2 · 17² · 23

Field	Data	Notes
Atkin-Lehner	2+ 17+ 23+	Signs for the Atkin-Lehner involutions
Class	13294a	Isogeny class
Conductor	13294	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	408600768032 = 25 · 176 · 232	Discriminant
Eigenvalues	2+  0 -4  4 -2 -2 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-49184,-4186016]	[a1,a2,a3,a4,a6]
Generators	[591:12854:1]	Generators of the group modulo torsion
j	545138290809/16928	j-invariant
L	2.4007741375437	L(r)(E,1)/r!
Ω	0.32058558345808	Real period
R	3.7443576090463	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	106352r2 119646cr2 46a2	Quadratic twists by: -4 -3 17

Hecke Eigenvalues for elliptic curve 13294a2

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
+	0	-4	4	-2	-2	+	-2	+	-2	0	4	-6	10	0	-4	12	8	-10	0	-6	12	14	-6	-6

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Quadratic twists for elliptic curve 13294a2

-4	-3	17
106352r2	119646cr2	46a2

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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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