Cremona's table of elliptic curves

34200 = 2³ · 3² · 5² · 19

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 19-	Signs for the Atkin-Lehner involutions
Class	34200z	Isogeny class
Conductor	34200	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	5921302500000000 = 28 · 38 · 510 · 192	Discriminant
Eigenvalues	2+ 3- 5+  0  0  2 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-427575,-107549750]	[a1,a2,a3,a4,a6]
Generators	[47973:1859264:27]	Generators of the group modulo torsion
j	2964647793616/2030625	j-invariant
L	5.7558976305268	L(r)(E,1)/r!
Ω	0.18670860513636	Real period
R	7.7070599214255	Regulator
r	1	Rank of the group of rational points
S	0.99999999999998	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	68400be2 11400bj2 6840r2	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 34200z2

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

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Quadratic twists for elliptic curve 34200z2

-4	-3	5
68400be2	11400bj2	6840r2

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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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