Cremona's table of elliptic curves

31768 = 2³ · 11 · 19²

Field	Data	Notes
Atkin-Lehner	2+ 11- 19-	Signs for the Atkin-Lehner involutions
Class	31768c	Isogeny class
Conductor	31768	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	448704	Modular degree for the optimal curve
Δ	-138120660655740928 = -1 · 211 · 11 · 1910	Discriminant
Eigenvalues	2+  2  0  2 11-  5  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1086008,-435614836]	[a1,a2,a3,a4,a6]
Generators	[2753234147320178708021635606481057804570096812368966525378483304716752014511645:-566288289029421794640342220126163366611511388779921540773070174112119383848345414:65039656524946022210235484481915218310863980890608307800150318211539880237]	Generators of the group modulo torsion
j	-11281250/11	j-invariant
L	9.1668334068188	L(r)(E,1)/r!
Ω	0.073941094901337	Real period
R	123.97481291088	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	63536d1 31768i1	Quadratic twists by: -4 -19

Hecke Eigenvalues for elliptic curve 31768c1

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	-	5	2	-	-8	-5	0	2	-2	-11	9	-2	-14	7	2	3	-4	0	-17	-7	-7

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Quadratic twists for elliptic curve 31768c1

-4	-19
63536d1	31768i1

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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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