Cremona's table of elliptic curves

17745 = 3 · 5 · 7 · 13²

Field	Data	Notes
Atkin-Lehner	3- 5- 7+ 13+	Signs for the Atkin-Lehner involutions
Class	17745s	Isogeny class
Conductor	17745	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	7148791984804981875 = 312 · 54 · 73 · 137	Discriminant
Eigenvalues	1 3- 5- 7+  4 13+  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-4083213,3172838281]	[a1,a2,a3,a4,a6]
Generators	[-325:66987:1]	Generators of the group modulo torsion
j	1559802282754777489/1481059636875	j-invariant
L	7.8101913004599	L(r)(E,1)/r!
Ω	0.23440349918122	Real period
R	2.7766192796258	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	53235i4 88725v4 124215g4 1365d3	Quadratic twists by: -3 5 -7 13

Hecke Eigenvalues for elliptic curve 17745s3

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	-	-	+	4	+	2	0	0	-10	4	-10	-6	-8	-4	-10	12	-10	4	0	-6	0	16	10	2

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Quadratic twists for elliptic curve 17745s3

-3	5	-7	13
53235i4	88725v4	124215g4	1365d3

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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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