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	30800g	Isogeny class
Conductor	30800	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	677600000000 = 211 · 58 · 7 · 112	Discriminant
Eigenvalues	2+ -2 5+ 7+ 11- -6 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-7008,219988]	[a1,a2,a3,a4,a6]
Generators	[-82:500:1] [-12:550:1]	Generators of the group modulo torsion
j	1189646642/21175	j-invariant
L	5.8761239066028	L(r)(E,1)/r!
Ω	0.90808202781476	Real period
R	0.8088646904432	Regulator
r	2	Rank of the group of rational points
S	0.99999999999989	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	15400r2 123200ee2 6160e2	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 30800g2

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	+	+	-	-6	-2	-2	-6	0	0	4	-8	-4	-4	-8	4	14	8	-12	-2	-6	0	-2	-12

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Quadratic twists for elliptic curve 30800g2

-4	8	5
15400r2	123200ee2	6160e2

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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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