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	68400ex	Isogeny class
Conductor	68400	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	98304	Modular degree for the optimal curve
Δ	2659392000000 = 212 · 37 · 56 · 19	Discriminant
Eigenvalues	2- 3- 5+  0  0 -6 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-5475,-134750]	[a1,a2,a3,a4,a6]
Generators	[-49:126:1] [-31:72:1]	Generators of the group modulo torsion
j	389017/57	j-invariant
L	10.320547304014	L(r)(E,1)/r!
Ω	0.56044768347917	Real period
R	2.301853412967	Regulator
r	2	Rank of the group of rational points
S	0.99999999999676	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4275e1 22800de1 2736t1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 68400ex1

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

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Quadratic twists for elliptic curve 68400ex1

-4	-3	5
4275e1	22800de1	2736t1

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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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