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	59150cg	Isogeny class
Conductor	59150	Conductor
∏ cp	256	Product of Tamagawa factors cp
deg	12779520	Modular degree for the optimal curve
Δ	3.2590595833053E+24	Discriminant
Eigenvalues	2-  2 5- 7- -2 13-  8 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-37171638,8043428531]	[a1,a2,a3,a4,a6]
Generators	[-3015:306007:1]	Generators of the group modulo torsion
j	274244925473/157351936	j-invariant
L	14.647219216485	L(r)(E,1)/r!
Ω	0.068022291851982	Real period
R	3.3645264519516	Regulator
r	1	Rank of the group of rational points
S	0.99999999999659	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	59150y1 59150x1	Quadratic twists by: 5 13

Hecke Eigenvalues for elliptic curve 59150cg1

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

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Quadratic twists for elliptic curve 59150cg1

5	13
59150y1	59150x1

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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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