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	78400ge	Isogeny class
Conductor	78400	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	92236816000000 = 210 · 56 · 78	Discriminant
Eigenvalues	2- -1 5+ 7+ -3  2 -3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-697433,224414737]	[a1,a2,a3,a4,a6]
j	406749952	j-invariant
L	1.5636883705657	L(r)(E,1)/r!
Ω	0.52122945886273	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	78400c2 19600bs2 3136o2 78400hl2	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 78400ge2

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	-1	3	6	7	-1	6	4	-9	3	9	1	7	0	1	13	-12	15	10

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Quadratic twists for elliptic curve 78400ge2

-4	8	5	-7
78400c2	19600bs2	3136o2	78400hl2

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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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