Cremona's table of elliptic curves

30800 = 2⁴ · 5² · 7 · 11

Field	Data	Notes
Atkin-Lehner	2- 5+ 7- 11-	Signs for the Atkin-Lehner involutions
Class	30800bz	Isogeny class
Conductor	30800	Conductor
∏ cp	288	Product of Tamagawa factors cp
Δ	-200436248320000000 = -1 · 214 · 57 · 76 · 113	Discriminant
Eigenvalues	2- -2 5+ 7- 11- -2 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-36008,21687988]	[a1,a2,a3,a4,a6]
Generators	[-252:3850:1] [78:-4400:1]	Generators of the group modulo torsion
j	-80677568161/3131816380	j-invariant
L	6.3707865241363	L(r)(E,1)/r!
Ω	0.26414552580941	Real period
R	0.33497878072104	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3850c3 123200fo3 6160k3	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 30800bz3

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	-6	-2	-6	0	-8	-8	0	-4	0	-12	-12	-10	-4	12	-14	10	0	-18	-8

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Quadratic twists for elliptic curve 30800bz3

-4	8	5
3850c3	123200fo3	6160k3

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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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