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	29400ek	Isogeny class
Conductor	29400	Conductor
∏ cp	252	Product of Tamagawa factors cp
deg	64512	Modular degree for the optimal curve
Δ	-840157920000 = -1 · 28 · 37 · 54 · 74	Discriminant
Eigenvalues	2- 3- 5- 7+ -6 -7 -4 -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-5308,153488]	[a1,a2,a3,a4,a6]
Generators	[-82:210:1] [128:-1260:1]	Generators of the group modulo torsion
j	-43061200/2187	j-invariant
L	9.1692606132687	L(r)(E,1)/r!
Ω	0.88085522478335	Real period
R	0.041307531352287	Regulator
r	2	Rank of the group of rational points
S	0.99999999999985	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	58800bq1 88200di1 29400c1 29400dp1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 29400ek1

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
-	-	-	+	-6	-7	-4	-5	-6	-4	-8	-1	-2	-4	8	-8	0	-5	5	4	1	11	-16	12	-11

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Quadratic twists for elliptic curve 29400ek1

-4	-3	5	-7
58800bq1	88200di1	29400c1	29400dp1

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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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