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	25200cd	Isogeny class
Conductor	25200	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	172032	Modular degree for the optimal curve
Δ	-2196674172630000 = -1 · 24 · 322 · 54 · 7	Discriminant
Eigenvalues	2+ 3- 5- 7+  5  2 -4 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-304275,-64641575]	[a1,a2,a3,a4,a6]
Generators	[24525567111419168:-1354541485377266559:7777691600797]	Generators of the group modulo torsion
j	-427361108435200/301327047	j-invariant
L	5.4560669304695	L(r)(E,1)/r!
Ω	0.10163297220653	Real period
R	26.842012055804	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	12600bh1 100800pb1 8400be1 25200bu1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 25200cd1

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
+	-	-	+	5	2	-4	-6	-1	-1	-2	5	0	7	-2	6	-6	0	-3	9	-12	-3	6	-6	-10

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Quadratic twists for elliptic curve 25200cd1

-4	8	-3	5
12600bh1	100800pb1	8400be1	25200bu1

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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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