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
Δ	71803584000000 = 212 · 310 · 56 · 19	Discriminant
Eigenvalues	2- 3- 5+  0  0 -6 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-365475,85041250]	[a1,a2,a3,a4,a6]
Generators	[335:450:1] [-190:12150:1]	Generators of the group modulo torsion
j	115714886617/1539	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	4275e3 22800de4 2736t3	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 68400ex4

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 68400ex4

-4	-3	5
4275e3	22800de4	2736t3

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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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