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	23232a	Isogeny class
Conductor	23232	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	50688	Modular degree for the optimal curve
Δ	28974461227008 = 212 · 3 · 119	Discriminant
Eigenvalues	2+ 3+  0  4 11+ -2 -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-8873,193833]	[a1,a2,a3,a4,a6]
Generators	[-81:612:1]	Generators of the group modulo torsion
j	8000/3	j-invariant
L	5.1640281972693	L(r)(E,1)/r!
Ω	0.60579923232037	Real period
R	4.2621613909031	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	23232bi1 11616i1 69696w1 23232b1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 23232a1

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

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Quadratic twists for elliptic curve 23232a1

-4	8	-3	-11
23232bi1	11616i1	69696w1	23232b1

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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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