Cremona's table of elliptic curves

6384 = 2⁴ · 3 · 7 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7- 19+	Signs for the Atkin-Lehner involutions
Class	6384d	Isogeny class
Conductor	6384	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	188160	Modular degree for the optimal curve
Δ	4339002922836599808 = 210 · 37 · 710 · 193	Discriminant
Eigenvalues	2+ 3+  2 7-  6 -2  0 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4955392,4246324048]	[a1,a2,a3,a4,a6]
j	13141891860831409148932/4237307541832617	j-invariant
L	2.4072261924954	L(r)(E,1)/r!
Ω	0.24072261924954	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3192g1 25536dr1 19152x1 44688bh1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6384d1

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	-	6	-2	0	+	4	-6	2	8	2	12	2	-6	-4	2	6	8	2	4	-4	-6	-8

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Quadratic twists for elliptic curve 6384d1

-4	8	-3	-7	-19
3192g1	25536dr1	19152x1	44688bh1	121296bn1

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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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