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	78400ho	Isogeny class
Conductor	78400	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1548288	Modular degree for the optimal curve
Δ	-1.2111126300875E+19	Discriminant
Eigenvalues	2-  1 5+ 7-  5 -5 -5  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-454883,-205040137]	[a1,a2,a3,a4,a6]
Generators	[18560680650706:10668231659612275:56181887]	Generators of the group modulo torsion
j	-88478050816/102942875	j-invariant
L	7.406687494765	L(r)(E,1)/r!
Ω	0.08796544506075	Real period
R	21.049991532612	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	78400hz1 39200ca1 15680dq1 11200ca1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 78400ho1

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	+	-	5	-5	-5	0	8	1	2	4	-2	-4	-13	-8	-4	-2	8	12	-6	-11	8	18	-5

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Quadratic twists for elliptic curve 78400ho1

-4	8	5	-7
78400hz1	39200ca1	15680dq1	11200ca1

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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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