Cremona's table of elliptic curves

11830 = 2 · 5 · 7 · 13²

Field	Data	Notes
Atkin-Lehner	2- 5- 7+ 13+	Signs for the Atkin-Lehner involutions
Class	11830x	Isogeny class
Conductor	11830	Conductor
∏ cp	72	Product of Tamagawa factors cp
Δ	59058402212264000 = 26 · 53 · 76 · 137	Discriminant
Eigenvalues	2- -2 5- 7+  0 13+  0 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-160300,-21774000]	[a1,a2,a3,a4,a6]
Generators	[-230:1830:1]	Generators of the group modulo torsion
j	94376601570889/12235496000	j-invariant
L	4.9078158888399	L(r)(E,1)/r!
Ω	0.24063668416713	Real period
R	1.1330626467555	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	94640dc3 106470s3 59150n3 82810ca3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 11830x3

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

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Quadratic twists for elliptic curve 11830x3

-4	-3	5	-7	13
94640dc3	106470s3	59150n3	82810ca3	910c3

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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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