Cremona's table of elliptic curves

13475 = 5² · 7² · 11

Field	Data	Notes
Atkin-Lehner	5+ 7- 11-	Signs for the Atkin-Lehner involutions
Class	13475h	Isogeny class
Conductor	13475	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	3538661328125 = 58 · 77 · 11	Discriminant
Eigenvalues	1  0 5+ 7- 11- -6  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-12576692,-17163988409]	[a1,a2,a3,a4,a6]
Generators	[2502408293378422594:-312461773196092411433:153491301696088]	Generators of the group modulo torsion
j	119678115308998401/1925	j-invariant
L	5.065712876796	L(r)(E,1)/r!
Ω	0.080169273266075	Real period
R	31.593855541033	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	121275dj4 2695c3 1925e4	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 13475h3

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

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Quadratic twists for elliptic curve 13475h3

-3	5	-7
121275dj4	2695c3	1925e4

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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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