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	59150d	Isogeny class
Conductor	59150	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	55296	Modular degree for the optimal curve
Δ	33641562500 = 22 · 57 · 72 · 133	Discriminant
Eigenvalues	2+  0 5+ 7+  2 13- -6  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1442,-18784]	[a1,a2,a3,a4,a6]
Generators	[-26:38:1] [-178:439:8]	Generators of the group modulo torsion
j	9663597/980	j-invariant
L	7.3056096863569	L(r)(E,1)/r!
Ω	0.77978489824665	Real period
R	1.1710937373212	Regulator
r	2	Rank of the group of rational points
S	1.0000000000003	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	11830r1 59150ca1	Quadratic twists by: 5 13

Hecke Eigenvalues for elliptic curve 59150d1

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
+	0	+	+	2	-	-6	6	-6	-10	-4	2	-4	-4	0	-12	-2	-10	-12	0	-14	-8	12	0	-2

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Quadratic twists for elliptic curve 59150d1

5	13
11830r1	59150ca1

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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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