Cremona's table of elliptic curves

52800 = 2⁶ · 3 · 5² · 11

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 11-	Signs for the Atkin-Lehner involutions
Class	52800bz	Isogeny class
Conductor	52800	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	-159720000 = -1 · 26 · 3 · 54 · 113	Discriminant
Eigenvalues	2+ 3+ 5- -3 11-  4 -3  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-208,-1238]	[a1,a2,a3,a4,a6]
Generators	[27:110:1]	Generators of the group modulo torsion
j	-25000000/3993	j-invariant
L	4.9890929804266	L(r)(E,1)/r!
Ω	0.62285134917046	Real period
R	0.89000957488683	Regulator
r	1	Rank of the group of rational points
S	0.99999999999811	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	52800dr1 26400ce1 52800dd1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 52800bz1

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
+	+	-	-3	-	4	-3	5	7	2	-4	11	-1	8	1	-10	5	-10	-6	-5	-2	-3	-4	-14	-13

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Quadratic twists for elliptic curve 52800bz1

-4	8	5
52800dr1	26400ce1	52800dd1

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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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