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	8040h	Isogeny class
Conductor	8040	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	5376	Modular degree for the optimal curve
Δ	-34732800 = -1 · 28 · 34 · 52 · 67	Discriminant
Eigenvalues	2- 3+ 5-  2  2  2 -7  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-7985,277317]	[a1,a2,a3,a4,a6]
Generators	[59:90:1]	Generators of the group modulo torsion
j	-219969716909056/135675	j-invariant
L	4.2608828029896	L(r)(E,1)/r!
Ω	1.7045717201974	Real period
R	0.31245992413392	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	16080k1 64320bc1 24120f1 40200m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8040h1

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	2	2	-7	1	1	-1	-4	-7	-6	-2	-1	0	-9	-8	+	-12	7	-8	-12	15	14

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Quadratic twists for elliptic curve 8040h1

-4	8	-3	5
16080k1	64320bc1	24120f1	40200m1

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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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