Cremona's table of elliptic curves

1189 = 29 · 41

Field	Data	Notes
Atkin-Lehner	29+ 41-	Signs for the Atkin-Lehner involutions
Class	1189a	Isogeny class
Conductor	1189	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	80	Modular degree for the optimal curve
Δ	-48749 = -1 · 29 · 412	Discriminant
Eigenvalues	1 -1  3  0  1  3  0  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-31,-82]	[a1,a2,a3,a4,a6]
j	-3463512697/48749	j-invariant
L	2.0131984829705	L(r)(E,1)/r!
Ω	1.0065992414853	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	19024b1 76096d1 10701a1 29725a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1189a1

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	-1	3	0	1	3	0	4	6	+	5	-2	-	-5	3	13	4	10	0	-6	4	1	-2	0	10

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Quadratic twists for elliptic curve 1189a1

-4	8	-3	5	-7	29	41
19024b1	76096d1	10701a1	29725a1	58261d1	34481a1	48749b1

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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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