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	8040d	Isogeny class
Conductor	8040	Conductor
∏ cp	20	Product of Tamagawa factors cp
Δ	1696454150400000 = 211 · 310 · 55 · 672	Discriminant
Eigenvalues	2+ 3+ 5- -2  0 -2  4  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-138760,-19749908]	[a1,a2,a3,a4,a6]
Generators	[-211:300:1]	Generators of the group modulo torsion
j	144274561547032082/828346753125	j-invariant
L	3.5944340309429	L(r)(E,1)/r!
Ω	0.24744767460551	Real period
R	2.9052073628684	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	16080i2 64320y2 24120t2 40200bf2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8040d2

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

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Quadratic twists for elliptic curve 8040d2

-4	8	-3	5
16080i2	64320y2	24120t2	40200bf2

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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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