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
deg	22400	Modular degree for the optimal curve
Δ	162810000000000 = 210 · 35 · 510 · 67	Discriminant
Eigenvalues	2+ 3+ 5- -2  0 -2  4  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-13760,100092]	[a1,a2,a3,a4,a6]
Generators	[-86:800:1]	Generators of the group modulo torsion
j	281391269564164/158994140625	j-invariant
L	3.5944340309429	L(r)(E,1)/r!
Ω	0.49489534921101	Real period
R	1.4526036814342	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	16080i1 64320y1 24120t1 40200bf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8040d1

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 8040d1

-4	8	-3	5
16080i1	64320y1	24120t1	40200bf1

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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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