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	20400q	Isogeny class
Conductor	20400	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	1586304000 = 210 · 36 · 53 · 17	Discriminant
Eigenvalues	2+ 3+ 5-  0 -2  0 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1768,-27968]	[a1,a2,a3,a4,a6]
Generators	[-24:8:1]	Generators of the group modulo torsion
j	4777559924/12393	j-invariant
L	4.1818441010076	L(r)(E,1)/r!
Ω	0.73633632593925	Real period
R	1.4198145445539	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	10200bp2 81600jo2 61200cd2 20400bl2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 20400q2

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
+	+	-	0	-2	0	-	4	0	-8	4	-2	0	-2	8	-2	-4	10	10	6	-10	-16	12	-6	-10

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Quadratic twists for elliptic curve 20400q2

-4	8	-3	5
10200bp2	81600jo2	61200cd2	20400bl2

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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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