Cremona's table of elliptic curves

38304 = 2⁵ · 3² · 7 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 19-	Signs for the Atkin-Lehner involutions
Class	38304n	Isogeny class
Conductor	38304	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	196608	Modular degree for the optimal curve
Δ	160504777226304 = 26 · 310 · 76 · 192	Discriminant
Eigenvalues	2+ 3- -2 7+  0 -2  6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-351921,80353240]	[a1,a2,a3,a4,a6]
Generators	[-523:11016:1]	Generators of the group modulo torsion
j	103312235477340352/3440174409	j-invariant
L	4.5769651672741	L(r)(E,1)/r!
Ω	0.53713677182603	Real period
R	4.2605211627149	Regulator
r	1	Rank of the group of rational points
S	0.99999999999995	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	38304r1 76608dv2 12768z1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 38304n1

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	-2	6	-	0	2	0	6	-6	0	8	-6	-4	2	4	-12	2	-4	-12	-14	-10

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Quadratic twists for elliptic curve 38304n1

-4	8	-3
38304r1	76608dv2	12768z1

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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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