Cremona's table of elliptic curves

29600 = 2⁵ · 5² · 37

Field	Data	Notes
Atkin-Lehner	2- 5+ 37-	Signs for the Atkin-Lehner involutions
Class	29600r	Isogeny class
Conductor	29600	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-87616000000 = -1 · 212 · 56 · 372	Discriminant
Eigenvalues	2-  0 5+  4  0 -2 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1100,-20000]	[a1,a2,a3,a4,a6]
Generators	[360:6800:1]	Generators of the group modulo torsion
j	-2299968/1369	j-invariant
L	5.8730544413145	L(r)(E,1)/r!
Ω	0.40349697191606	Real period
R	3.6388466643414	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	29600b2 59200b1 1184a2	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 29600r2

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
-	0	+	4	0	-2	-2	-2	6	-6	-2	-	-2	2	4	6	6	-6	8	-4	-14	2	4	-6	-10

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Quadratic twists for elliptic curve 29600r2

-4	8	5
29600b2	59200b1	1184a2

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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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