Cremona's table of elliptic curves

40200 = 2³ · 3 · 5² · 67

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 67+	Signs for the Atkin-Lehner involutions
Class	40200s	Isogeny class
Conductor	40200	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	129024	Modular degree for the optimal curve
Δ	-50516634700800 = -1 · 210 · 38 · 52 · 673	Discriminant
Eigenvalues	2- 3+ 5+  2  0  6  5 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-19928,1142172]	[a1,a2,a3,a4,a6]
j	-34189809689860/1973306043	j-invariant
L	2.4989005357756	L(r)(E,1)/r!
Ω	0.62472513396627	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	80400be1 120600k1 40200r1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 40200s1

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	0	6	5	-5	8	-3	-6	-9	-2	10	7	2	-9	0	+	-3	14	-2	-3	-1	-8

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Quadratic twists for elliptic curve 40200s1

-4	-3	5
80400be1	120600k1	40200r1

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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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