Cremona's table of elliptic curves

25800 = 2³ · 3 · 5² · 43

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 43-	Signs for the Atkin-Lehner involutions
Class	25800w	Isogeny class
Conductor	25800	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	6656400000000 = 210 · 32 · 58 · 432	Discriminant
Eigenvalues	2- 3+ 5+  4  4  2 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-14408,658812]	[a1,a2,a3,a4,a6]
Generators	[1238:43344:1]	Generators of the group modulo torsion
j	20674973956/416025	j-invariant
L	5.482868386535	L(r)(E,1)/r!
Ω	0.74982815433356	Real period
R	3.6560833004517	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	51600x2 77400o2 5160e2	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 25800w2

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

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Quadratic twists for elliptic curve 25800w2

-4	-3	5
51600x2	77400o2	5160e2

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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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