Cremona's table of elliptic curves

78400 = 2⁶ · 5² · 7²

Field	Data	Notes
Atkin-Lehner	2- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	78400hk	Isogeny class
Conductor	78400	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-181420519600947200 = -1 · 219 · 52 · 712	Discriminant
Eigenvalues	2-  1 5+ 7-  3 -2  3  7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-142753,-29218337]	[a1,a2,a3,a4,a6]
Generators	[403983:5747552:729]	Generators of the group modulo torsion
j	-417267265/235298	j-invariant
L	8.4391891650421	L(r)(E,1)/r!
Ω	0.1196811940183	Real period
R	8.8142389854187	Regulator
r	1	Rank of the group of rational points
S	0.99999999951912	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	78400bu2 19600ck2 78400kn2 11200cm2	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 78400hk2

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	+	-	3	-2	3	7	0	6	-4	8	9	-8	6	-12	-12	-10	7	-6	5	-14	-9	15	-10

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Quadratic twists for elliptic curve 78400hk2

-4	8	5	-7
78400bu2	19600ck2	78400kn2	11200cm2

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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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