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	8	Product of Tamagawa factors cp
Δ	30650669727744 = 219 · 3 · 117	Discriminant
Eigenvalues	2- 3+ -2 -4 11- -6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2726049,-1731493311]	[a1,a2,a3,a4,a6]
Generators	[105312:5850955:27]	Generators of the group modulo torsion
j	4824238966273/66	j-invariant
L	1.9472901347352	L(r)(E,1)/r!
Ω	0.11749411849186	Real period
R	8.2867557956531	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	23232cg4 5808bf3 69696gk4 2112u3	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 23232de4

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 23232de4

-4	8	-3	-11
23232cg4	5808bf3	69696gk4	2112u3

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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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