Cremona's table of elliptic curves

33600 = 2⁶ · 3 · 5² · 7

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 7+	Signs for the Atkin-Lehner involutions
Class	33600l	Isogeny class
Conductor	33600	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	147456	Modular degree for the optimal curve
Δ	-770703360000000 = -1 · 226 · 3 · 57 · 72	Discriminant
Eigenvalues	2+ 3+ 5+ 7+ -4 -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,15967,-1092063]	[a1,a2,a3,a4,a6]
Generators	[147:2100:1]	Generators of the group modulo torsion
j	109902239/188160	j-invariant
L	3.7820952770563	L(r)(E,1)/r!
Ω	0.26521745009987	Real period
R	1.7825445100012	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	33600gt1 1050g1 100800dy1 6720u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 33600l1

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	8	-6	-8	-2	2	-12	8	6	-4	2	12	8	14	0	12	2	-10

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Quadratic twists for elliptic curve 33600l1

-4	8	-3	5
33600gt1	1050g1	100800dy1	6720u1

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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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