Cremona's table of elliptic curves

125316 = 2² · 3² · 59²

Field	Data	Notes
Atkin-Lehner	2- 3- 59-	Signs for the Atkin-Lehner involutions
Class	125316i	Isogeny class
Conductor	125316	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	86400	Modular degree for the optimal curve
Δ	-17540229888 = -1 · 28 · 39 · 592	Discriminant
Eigenvalues	2- 3- -2  0 -2 -6  4  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1416,21476]	[a1,a2,a3,a4,a6]
Generators	[-11:189:1] [16:-54:1]	Generators of the group modulo torsion
j	-483328/27	j-invariant
L	10.426635314396	L(r)(E,1)/r!
Ω	1.2140122776796	Real period
R	0.71571457074232	Regulator
r	2	Rank of the group of rational points
S	1.000000000005	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	41772a1 125316h1	Quadratic twists by: -3 -59

Hecke Eigenvalues for elliptic curve 125316i1

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	-2	-6	4	1	-4	4	7	-11	-8	12	-10	-6	-	-7	-7	-6	-1	-7	16	-6	-17

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Quadratic twists for elliptic curve 125316i1

-3	-59
41772a1	125316h1

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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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