Cremona's table of elliptic curves

42400 = 2⁵ · 5² · 53

Field	Data	Notes
Atkin-Lehner	2- 5+ 53-	Signs for the Atkin-Lehner involutions
Class	42400k	Isogeny class
Conductor	42400	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	20480	Modular degree for the optimal curve
Δ	-3392000000 = -1 · 212 · 56 · 53	Discriminant
Eigenvalues	2- -1 5+ -4  0  3  3  7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,367,-863]	[a1,a2,a3,a4,a6]
Generators	[17:-100:1]	Generators of the group modulo torsion
j	85184/53	j-invariant
L	3.7315330758123	L(r)(E,1)/r!
Ω	0.81328834124436	Real period
R	0.57352553924868	Regulator
r	1	Rank of the group of rational points
S	0.99999999999936	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	42400b1 84800c1 1696a1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 42400k1

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	+	-4	0	3	3	7	-3	-7	-4	11	-6	2	6	-	-14	-12	-12	5	-8	-5	5	10	7

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Quadratic twists for elliptic curve 42400k1

-4	8	5
42400b1	84800c1	1696a1

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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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