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	34974454662875000 = 23 · 56 · 73 · 138	Discriminant
Eigenvalues	2- -2 5- 7+  0 13+  0 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2478980,-1502483048]	[a1,a2,a3,a4,a6]
Generators	[-906:478:1]	Generators of the group modulo torsion
j	349046010201856969/7245875000	j-invariant
L	4.9078158888399	L(r)(E,1)/r!
Ω	0.12031834208357	Real period
R	2.2661252935111	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	94640dc4 106470s4 59150n4 82810ca4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 11830x4

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 11830x4

-4	-3	5	-7	13
94640dc4	106470s4	59150n4	82810ca4	910c4

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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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