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	30800o	Isogeny class
Conductor	30800	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	16384	Modular degree for the optimal curve
Δ	-3388000000 = -1 · 28 · 56 · 7 · 112	Discriminant
Eigenvalues	2+ -2 5+ 7- 11- -4  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-308,3388]	[a1,a2,a3,a4,a6]
Generators	[3:50:1]	Generators of the group modulo torsion
j	-810448/847	j-invariant
L	3.7844942094266	L(r)(E,1)/r!
Ω	1.2826720065664	Real period
R	1.4752384826568	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	15400l1 123200fq1 1232c1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 30800o1

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	+	-	-	-4	0	4	4	10	-2	-10	0	4	-2	-2	-6	0	-8	-12	12	-16	-4	-6	10

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Quadratic twists for elliptic curve 30800o1

-4	8	5
15400l1	123200fq1	1232c1

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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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