Cremona's table of elliptic curves

68400 = 2⁴ · 3² · 5² · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 19+	Signs for the Atkin-Lehner involutions
Class	68400b	Isogeny class
Conductor	68400	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-113689008000000 = -1 · 210 · 39 · 56 · 192	Discriminant
Eigenvalues	2+ 3+ 5+  0 -2  2 -4 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,10125,-330750]	[a1,a2,a3,a4,a6]
Generators	[49:532:1]	Generators of the group modulo torsion
j	364500/361	j-invariant
L	6.0109279508121	L(r)(E,1)/r!
Ω	0.32225099377205	Real period
R	2.3316173056364	Regulator
r	1	Rank of the group of rational points
S	1.0000000000187	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	34200ca2 68400a2 2736b2	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 68400b2

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	2	-4	+	2	6	-4	-2	-2	4	10	-6	-4	2	4	-4	6	-8	-2	6	10

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Quadratic twists for elliptic curve 68400b2

-4	-3	5
34200ca2	68400a2	2736b2

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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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