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
deg	6144	Modular degree for the optimal curve
Δ	20100000000 = 28 · 3 · 58 · 67	Discriminant
Eigenvalues	2- 3+ 5- -4 -4  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-900,-7548]	[a1,a2,a3,a4,a6]
Generators	[-11:30:1]	Generators of the group modulo torsion
j	315278049616/78515625	j-invariant
L	3.2310006885109	L(r)(E,1)/r!
Ω	0.88746897999367	Real period
R	1.8203457029754	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	16080l1 64320bf1 24120i1 40200n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8040i1

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 8040i1

-4	8	-3	5
16080l1	64320bf1	24120i1	40200n1

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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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