Cremona's table of elliptic curves

10164 = 2² · 3 · 7 · 11²

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 11-	Signs for the Atkin-Lehner involutions
Class	10164v	Isogeny class
Conductor	10164	Conductor
∏ cp	171	Product of Tamagawa factors cp
deg	65664	Modular degree for the optimal curve
Δ	12348758442214656 = 28 · 319 · 73 · 112	Discriminant
Eigenvalues	2- 3- -1 7- 11- -4  5  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-58021,-612889]	[a1,a2,a3,a4,a6]
Generators	[-223:1134:1]	Generators of the group modulo torsion
j	697367157735424/398655683181	j-invariant
L	5.2301557879776	L(r)(E,1)/r!
Ω	0.33323805774053	Real period
R	0.091783353227489	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	40656bh1 30492bg1 71148q1 10164q1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 10164v1

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
-	-	-1	-	-	-4	5	6	0	-10	-2	-2	-2	-13	1	4	-3	8	3	-16	-12	8	-7	1	-2

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Quadratic twists for elliptic curve 10164v1

-4	-3	-7	-11
40656bh1	30492bg1	71148q1	10164q1

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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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