Cremona's table of elliptic curves

20400 = 2⁴ · 3 · 5² · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 17-	Signs for the Atkin-Lehner involutions
Class	20400bk	Isogeny class
Conductor	20400	Conductor
∏ cp	448	Product of Tamagawa factors cp
deg	1290240	Modular degree for the optimal curve
Δ	-7.6279907617335E+21	Discriminant
Eigenvalues	2+ 3- 5+ -4  0 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-505908,-4204519812]	[a1,a2,a3,a4,a6]
Generators	[3078:153000:1]	Generators of the group modulo torsion
j	-3579968623693264/1906997690433375	j-invariant
L	5.205868782693	L(r)(E,1)/r!
Ω	0.059253601082659	Real period
R	0.78444129006107	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	10200bd1 81600gs1 61200bp1 4080d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 20400bk1

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

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Quadratic twists for elliptic curve 20400bk1

-4	8	-3	5
10200bd1	81600gs1	61200bp1	4080d1

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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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