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	30800bi	Isogeny class
Conductor	30800	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	275968000000 = 215 · 56 · 72 · 11	Discriminant
Eigenvalues	2-  0 5+ 7+ 11- -2  4  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-187675,-31293750]	[a1,a2,a3,a4,a6]
Generators	[888153:44516058:343]	Generators of the group modulo torsion
j	11422548526761/4312	j-invariant
L	5.115107877993	L(r)(E,1)/r!
Ω	0.22937599123594	Real period
R	11.150050732056	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	3850r2 123200dy2 1232k2	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 30800bi2

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

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Quadratic twists for elliptic curve 30800bi2

-4	8	5
3850r2	123200dy2	1232k2

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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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