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	78400p	Isogeny class
Conductor	78400	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	3870720	Modular degree for the optimal curve
Δ	-472252497920000000 = -1 · 220 · 57 · 78	Discriminant
Eigenvalues	2+  3 5+ 7+  2  0  4  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-10324300,12768518000]	[a1,a2,a3,a4,a6]
Generators	[49980:9800:27]	Generators of the group modulo torsion
j	-5154200289/20	j-invariant
L	13.308375409489	L(r)(E,1)/r!
Ω	0.25961190080665	Real period
R	2.1359407655527	Regulator
r	1	Rank of the group of rational points
S	0.9999999998314	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	78400go1 2450c1 15680bl1 78400dk1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 78400p1

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	+	+	2	0	4	6	-3	-9	-4	-4	-7	-5	-8	-2	-10	-1	-9	2	4	10	-7	1	-14

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Quadratic twists for elliptic curve 78400p1

-4	8	5	-7
78400go1	2450c1	15680bl1	78400dk1

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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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