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	20400bo	Isogeny class
Conductor	20400	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-918000 = -1 · 24 · 33 · 53 · 17	Discriminant
Eigenvalues	2+ 3- 5- -3  1  0 17+  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-728,7323]	[a1,a2,a3,a4,a6]
Generators	[13:15:1]	Generators of the group modulo torsion
j	-21364083968/459	j-invariant
L	5.698020435267	L(r)(E,1)/r!
Ω	2.5824236663845	Real period
R	0.36774371490875	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	10200l1 81600he1 61200ct1 20400s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 20400bo1

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	1	0	+	1	0	7	-2	-1	-9	2	1	11	-10	-8	2	0	1	-10	-12	6	10

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Quadratic twists for elliptic curve 20400bo1

-4	8	-3	5
10200l1	81600he1	61200ct1	20400s1

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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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