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	23232cq	Isogeny class
Conductor	23232	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-12266496 = -1 · 210 · 32 · 113	Discriminant
Eigenvalues	2- 3+ -2 -2 11+  0 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-29,189]	[a1,a2,a3,a4,a6]
Generators	[-4:15:1] [4:11:1]	Generators of the group modulo torsion
j	-2048/9	j-invariant
L	5.8113895742839	L(r)(E,1)/r!
Ω	1.9610646429491	Real period
R	1.4816925069705	Regulator
r	2	Rank of the group of rational points
S	0.99999999999978	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	23232bj1 5808i1 69696fe1 23232cp1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 23232cq1

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	-2	+	0	-6	-6	4	-2	8	-2	-10	-10	0	-6	0	-4	-4	0	-4	-10	-12	18	18

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Quadratic twists for elliptic curve 23232cq1

-4	8	-3	-11
23232bj1	5808i1	69696fe1	23232cp1

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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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