Cremona's table of elliptic curves

25200 = 2⁴ · 3² · 5² · 7

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 7-	Signs for the Atkin-Lehner involutions
Class	25200t	Isogeny class
Conductor	25200	Conductor
∏ cp	84	Product of Tamagawa factors cp
deg	177408	Modular degree for the optimal curve
Δ	-20748539992320000 = -1 · 211 · 39 · 54 · 77	Discriminant
Eigenvalues	2+ 3+ 5- 7- -4  1  3  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-76275,-10666350]	[a1,a2,a3,a4,a6]
Generators	[615:-13230:1]	Generators of the group modulo torsion
j	-1947910950/823543	j-invariant
L	5.5633931103087	L(r)(E,1)/r!
Ω	0.14073228201148	Real period
R	0.47061604781918	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	12600i1 100800kr1 25200s1 25200i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 25200t1

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	1	3	6	3	-3	-9	6	5	-9	-6	-9	13	-7	-8	16	-8	-12	-15	14	-8

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Quadratic twists for elliptic curve 25200t1

-4	8	-3	5
12600i1	100800kr1	25200s1	25200i1

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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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