Cremona's table of elliptic curves

23232 = 2⁶ · 3 · 11²

Field	Data	Notes
Atkin-Lehner	2- 3+ 11-	Signs for the Atkin-Lehner involutions
Class	23232de	Isogeny class
Conductor	23232	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	2022944202031104 = 220 · 32 · 118	Discriminant
Eigenvalues	2- 3+ -2 -4 11- -6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-170529,-26961471]	[a1,a2,a3,a4,a6]
Generators	[-245:228:1]	Generators of the group modulo torsion
j	1180932193/4356	j-invariant
L	1.9472901347352	L(r)(E,1)/r!
Ω	0.23498823698373	Real period
R	4.1433778978265	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	23232cg2 5808bf2 69696gk2 2112u2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 23232de2

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

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Quadratic twists for elliptic curve 23232de2

-4	8	-3	-11
23232cg2	5808bf2	69696gk2	2112u2

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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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