Cremona's table of elliptic curves

7200 = 2⁵ · 3² · 5²

Field	Data	Notes
Atkin-Lehner	2- 3- 5+	Signs for the Atkin-Lehner involutions
Class	7200bp	Isogeny class
Conductor	7200	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	1476225000000 = 26 · 310 · 58	Discriminant
Eigenvalues	2- 3- 5+ -4  0  2 -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-6825,209000]	[a1,a2,a3,a4,a6]
Generators	[-41:648:1]	Generators of the group modulo torsion
j	48228544/2025	j-invariant
L	3.6072816791836	L(r)(E,1)/r!
Ω	0.84200135834621	Real period
R	2.1420878027256	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	7200bn1 14400eg2 2400d1 1440d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7200bp1

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	0	2	-6	0	4	2	8	-6	6	12	12	-10	8	-10	-12	8	-10	-16	-12	6	-18

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Quadratic twists for elliptic curve 7200bp1

-4	8	-3	5
7200bn1	14400eg2	2400d1	1440d1

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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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