Cremona's table of elliptic curves

86640 = 2⁴ · 3 · 5 · 19²

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 19-	Signs for the Atkin-Lehner involutions
Class	86640bh	Isogeny class
Conductor	86640	Conductor
∏ cp	216	Product of Tamagawa factors cp
deg	311040	Modular degree for the optimal curve
Δ	-113689008000000 = -1 · 210 · 39 · 56 · 192	Discriminant
Eigenvalues	2+ 3- 5- -3 -2 -1 -8 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-21400,1302500]	[a1,a2,a3,a4,a6]
Generators	[110:540:1] [-142:1224:1]	Generators of the group modulo torsion
j	-2932095879364/307546875	j-invariant
L	12.694576914674	L(r)(E,1)/r!
Ω	0.57680042004597	Real period
R	0.10189172437821	Regulator
r	2	Rank of the group of rational points
S	0.99999999998682	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	43320y1 86640g1	Quadratic twists by: -4 -19

Hecke Eigenvalues for elliptic curve 86640bh1

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
+	-	-	-3	-2	-1	-8	-	-2	-6	-11	1	2	5	-4	0	-14	-7	-5	-8	3	-7	-10	0	-14

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Quadratic twists for elliptic curve 86640bh1

-4	-19
43320y1	86640g1

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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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