Cremona's table of elliptic curves

17430 = 2 · 3 · 5 · 7 · 83

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 7- 83-	Signs for the Atkin-Lehner involutions
Class	17430be	Isogeny class
Conductor	17430	Conductor
∏ cp	189	Product of Tamagawa factors cp
deg	72576	Modular degree for the optimal curve
Δ	-13123981248000 = -1 · 29 · 3 · 53 · 77 · 83	Discriminant
Eigenvalues	2- 3+ 5- 7- -5  3  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-18060,942765]	[a1,a2,a3,a4,a6]
Generators	[93:-327:1]	Generators of the group modulo torsion
j	-651446046858075841/13123981248000	j-invariant
L	7.0513510815192	L(r)(E,1)/r!
Ω	0.70883026688182	Real period
R	0.052634230822531	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	52290x1 87150bd1 122010cv1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 17430be1

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
-	+	-	-	-5	3	0	2	4	5	-8	-10	7	-8	-13	-13	-6	-7	-6	-1	12	2	-	-16	4

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Quadratic twists for elliptic curve 17430be1

-3	5	-7
52290x1	87150bd1	122010cv1

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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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