Cremona's table of elliptic curves

59150 = 2 · 5² · 7 · 13²

Field	Data	Notes
Atkin-Lehner	2- 5+ 7- 13+	Signs for the Atkin-Lehner involutions
Class	59150bx	Isogeny class
Conductor	59150	Conductor
∏ cp	144	Product of Tamagawa factors cp
Δ	1142023009400000000 = 29 · 58 · 7 · 138	Discriminant
Eigenvalues	2-  2 5+ 7-  0 13+  0 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-80765188,279339339781]	[a1,a2,a3,a4,a6]
Generators	[140223:-87701:27]	Generators of the group modulo torsion
j	772531501373731009/15142400	j-invariant
L	14.486166114374	L(r)(E,1)/r!
Ω	0.1976179498455	Real period
R	2.0362193995431	Regulator
r	1	Rank of the group of rational points
S	1.0000000000092	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	11830i2 4550c2	Quadratic twists by: 5 13

Hecke Eigenvalues for elliptic curve 59150bx2

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

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Quadratic twists for elliptic curve 59150bx2

5	13
11830i2	4550c2

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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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