Cremona's table of elliptic curves

10080 = 2⁵ · 3² · 5 · 7

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 7-	Signs for the Atkin-Lehner involutions
Class	10080f	Isogeny class
Conductor	10080	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	19752284160 = 212 · 39 · 5 · 72	Discriminant
Eigenvalues	2+ 3+ 5- 7-  0 -4 -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-972,9504]	[a1,a2,a3,a4,a6]
Generators	[-30:108:1]	Generators of the group modulo torsion
j	1259712/245	j-invariant
L	4.8299066345055	L(r)(E,1)/r!
Ω	1.1555697952121	Real period
R	1.0449188475065	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	10080bi2 20160i1 10080be2 50400ce2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10080f2

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
+	+	-	-	0	-4	-2	2	-2	4	-10	6	-6	4	12	-6	-12	6	-4	4	-8	0	-4	18	-12

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Quadratic twists for elliptic curve 10080f2

-4	8	-3	5	-7
10080bi2	20160i1	10080be2	50400ce2	70560d2

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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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