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	78400lm	Isogeny class
Conductor	78400	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	645120	Modular degree for the optimal curve
Δ	-42875000000 = -1 · 26 · 59 · 73	Discriminant
Eigenvalues	2- -3 5- 7-  3 -3 -7 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-274750,55431250]	[a1,a2,a3,a4,a6]
Generators	[-475:8875:1] [301:49:1]	Generators of the group modulo torsion
j	-53497400832	j-invariant
L	6.6437537709327	L(r)(E,1)/r!
Ω	0.81984769860303	Real period
R	2.0259109656026	Regulator
r	2	Rank of the group of rational points
S	1.0000000000056	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	78400lg1 39200da1 78400lf1 78400le1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 78400lm1

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
-	-3	-	-	3	-3	-7	-6	-6	1	6	-6	-10	6	3	4	-12	-6	-12	0	6	15	-12	2	9

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Quadratic twists for elliptic curve 78400lm1

-4	8	5	-7
78400lg1	39200da1	78400lf1	78400le1

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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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