Cremona's table of elliptic curves

39600 = 2⁴ · 3² · 5² · 11

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 11-	Signs for the Atkin-Lehner involutions
Class	39600bg	Isogeny class
Conductor	39600	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	98304	Modular degree for the optimal curve
Δ	120074501250000 = 24 · 38 · 57 · 114	Discriminant
Eigenvalues	2+ 3- 5+  4 11- -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-12450,-89125]	[a1,a2,a3,a4,a6]
Generators	[-862:297:8]	Generators of the group modulo torsion
j	1171019776/658845	j-invariant
L	6.8056575474088	L(r)(E,1)/r!
Ω	0.48640105683654	Real period
R	3.4979660568969	Regulator
r	1	Rank of the group of rational points
S	0.99999999999955	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	19800bg1 13200g1 7920j1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 39600bg1

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	-	-2	-2	-4	0	2	0	2	6	0	-8	-2	4	-10	4	0	-14	-16	0	-10	6

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Quadratic twists for elliptic curve 39600bg1

-4	-3	5
19800bg1	13200g1	7920j1

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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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