Cremona's table of elliptic curves

8040 = 2³ · 3 · 5 · 67

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 67+	Signs for the Atkin-Lehner involutions
Class	8040i	Isogeny class
Conductor	8040	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	25856640000 = 210 · 32 · 54 · 672	Discriminant
Eigenvalues	2- 3+ 5- -4 -4  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-13400,-592548]	[a1,a2,a3,a4,a6]
Generators	[294:4560:1]	Generators of the group modulo torsion
j	259878624962404/25250625	j-invariant
L	3.2310006885109	L(r)(E,1)/r!
Ω	0.44373448999684	Real period
R	3.6406914059508	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	16080l2 64320bf2 24120i2 40200n2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8040i2

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
-	+	-	-4	-4	2	2	4	4	2	-4	-10	-6	4	-4	6	-12	10	+	12	10	4	12	-6	2

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Quadratic twists for elliptic curve 8040i2

-4	8	-3	5
16080l2	64320bf2	24120i2	40200n2

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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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