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	10164g	Isogeny class
Conductor	10164	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	12672	Modular degree for the optimal curve
Δ	1152393344256 = 28 · 3 · 7 · 118	Discriminant
Eigenvalues	2- 3+  3 7+ 11- -2 -1  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3549,-61719]	[a1,a2,a3,a4,a6]
Generators	[-40:121:1]	Generators of the group modulo torsion
j	90112/21	j-invariant
L	4.4666151132011	L(r)(E,1)/r!
Ω	0.6289325851895	Real period
R	0.78909978560567	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	40656dl1 30492w1 71148cr1 10164m1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 10164g1

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
-	+	3	+	-	-2	-1	0	2	-4	6	-6	-6	1	-7	0	1	-6	11	-6	6	-12	11	13	-8

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Quadratic twists for elliptic curve 10164g1

-4	-3	-7	-11
40656dl1	30492w1	71148cr1	10164m1

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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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