Cremona's table of elliptic curves

13328 = 2⁴ · 7² · 17

Field	Data	Notes
Atkin-Lehner	2- 7- 17+	Signs for the Atkin-Lehner involutions
Class	13328o	Isogeny class
Conductor	13328	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	8192135168 = 212 · 76 · 17	Discriminant
Eigenvalues	2-  0  2 7-  0  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-71099,-7296982]	[a1,a2,a3,a4,a6]
Generators	[49195:633438:125]	Generators of the group modulo torsion
j	82483294977/17	j-invariant
L	5.1639100948877	L(r)(E,1)/r!
Ω	0.2923705918771	Real period
R	8.8311038085842	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	833a3 53312bt4 119952go4 272b3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13328o3

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

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Quadratic twists for elliptic curve 13328o3

-4	8	-3	-7
833a3	53312bt4	119952go4	272b3

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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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