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	33600bx	Isogeny class
Conductor	33600	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	109824	Modular degree for the optimal curve
Δ	-228562145280000 = -1 · 215 · 313 · 54 · 7	Discriminant
Eigenvalues	2+ 3+ 5- 7-  2  3  1  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,7167,-691263]	[a1,a2,a3,a4,a6]
Generators	[521:12008:1]	Generators of the group modulo torsion
j	1987675000/11160261	j-invariant
L	5.3751016032999	L(r)(E,1)/r!
Ω	0.27997027685325	Real period
R	4.7997073686835	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	33600di1 16800cb1 100800hu1 33600cg1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 33600bx1

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	3	1	4	-9	-3	5	-6	3	-13	4	-1	15	-1	4	-12	2	14	7	-10	-6

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Quadratic twists for elliptic curve 33600bx1

-4	8	-3	5
33600di1	16800cb1	100800hu1	33600cg1

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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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