Cremona's table of elliptic curves

29400 = 2³ · 3 · 5² · 7²

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7+	Signs for the Atkin-Lehner involutions
Class	29400du	Isogeny class
Conductor	29400	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	161280	Modular degree for the optimal curve
Δ	-8301313440000000 = -1 · 211 · 32 · 57 · 78	Discriminant
Eigenvalues	2- 3- 5+ 7+  3 -1  0 -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,48592,-1473312]	[a1,a2,a3,a4,a6]
Generators	[403:9150:1]	Generators of the group modulo torsion
j	68782/45	j-invariant
L	7.024495204855	L(r)(E,1)/r!
Ω	0.23624271505754	Real period
R	3.7167787391583	Regulator
r	1	Rank of the group of rational points
S	0.99999999999999	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	58800j1 88200bi1 5880b1 29400cu1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 29400du1

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	-1	0	-7	5	0	6	-3	-3	-8	1	-5	-4	-8	0	-6	14	-16	16	6	-16

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Quadratic twists for elliptic curve 29400du1

-4	-3	5	-7
58800j1	88200bi1	5880b1	29400cu1

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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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