Cremona's table of elliptic curves

29664 = 2⁵ · 3² · 103

Field	Data	Notes
Atkin-Lehner	2+ 3- 103-	Signs for the Atkin-Lehner involutions
Class	29664d	Isogeny class
Conductor	29664	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	-8304021504 = -1 · 212 · 39 · 103	Discriminant
Eigenvalues	2+ 3-  3 -2  6 -5  4  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-156,-4448]	[a1,a2,a3,a4,a6]
Generators	[53:369:1]	Generators of the group modulo torsion
j	-140608/2781	j-invariant
L	6.9228086	L(r)(E,1)/r!
Ω	0.56443653851619	Real period
R	3.0662475440547	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	29664f1 59328w1 9888j1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 29664d1

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
+	-	3	-2	6	-5	4	0	1	-2	-7	-6	0	-7	-2	10	-3	-5	7	4	0	-10	9	-6	-7

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Quadratic twists for elliptic curve 29664d1

-4	8	-3
29664f1	59328w1	9888j1

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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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