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	33600hj	Isogeny class
Conductor	33600	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	368640	Modular degree for the optimal curve
Δ	134873088000000000 = 226 · 3 · 59 · 73	Discriminant
Eigenvalues	2- 3- 5- 7-  2 -6  4 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-128833,-2185537]	[a1,a2,a3,a4,a6]
Generators	[9199:881664:1]	Generators of the group modulo torsion
j	461889917/263424	j-invariant
L	7.1690913277099	L(r)(E,1)/r!
Ω	0.27266182795134	Real period
R	4.3821629290609	Regulator
r	1	Rank of the group of rational points
S	0.99999999999997	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	33600bn1 8400bv1 100800pr1 33600fk1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 33600hj1

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

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Quadratic twists for elliptic curve 33600hj1

-4	8	-3	5
33600bn1	8400bv1	100800pr1	33600fk1

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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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