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	11830d	Isogeny class
Conductor	11830	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	188160	Modular degree for the optimal curve
Δ	157423479449600000 = 214 · 55 · 72 · 137	Discriminant
Eigenvalues	2+ -2 5+ 7-  4 13+  0  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-193509,26612432]	[a1,a2,a3,a4,a6]
j	166021325905681/32614400000	j-invariant
L	1.2289801064491	L(r)(E,1)/r!
Ω	0.30724502661227	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	94640bv1 106470ga1 59150bk1 82810bk1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 11830d1

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	6	-2	6	8	6	8	4	8	0	10	-14	4	-6	-10	16	0	16	-14

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Quadratic twists for elliptic curve 11830d1

-4	-3	5	-7	13
94640bv1	106470ga1	59150bk1	82810bk1	910k1

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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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