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	78400is	Isogeny class
Conductor	78400	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	439040000000000 = 217 · 510 · 73	Discriminant
Eigenvalues	2- -2 5+ 7-  4  2  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-24033,-1027937]	[a1,a2,a3,a4,a6]
Generators	[-57:400:1]	Generators of the group modulo torsion
j	2185454/625	j-invariant
L	4.3595285402606	L(r)(E,1)/r!
Ω	0.39178799525805	Real period
R	1.3909080273189	Regulator
r	1	Rank of the group of rational points
S	0.99999999985499	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	78400cn2 19600u2 15680cs2 78400ig2	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 78400is2

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
-	-2	+	-	4	2	0	2	-4	-10	-4	-2	-12	4	4	2	10	-6	-4	12	4	4	-14	8	8

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Quadratic twists for elliptic curve 78400is2

-4	8	5	-7
78400cn2	19600u2	15680cs2	78400ig2

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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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