Cremona's table of elliptic curves

232 = 2³ · 29

Field	Data	Notes
Atkin-Lehner	2+ 29+	Signs for the Atkin-Lehner involutions
Class	232a	Isogeny class
Conductor	232	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	-29696 = -1 · 210 · 29	Discriminant
Eigenvalues	2+ -1 -3  2 -3 -5 -4  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,8,-4]	[a1,a2,a3,a4,a6]
Generators	[2:4:1]	Generators of the group modulo torsion
j	48668/29	j-invariant
L	1.2149825684911	L(r)(E,1)/r!
Ω	2.173832562827	Real period
R	0.27945633653382	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	464a1 1856b1 2088m1 5800g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 232a1

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
+	-1	-3	2	-3	-5	-4	0	0	+	9	8	-2	-11	-7	9	4	-12	12	2	-4	3	-16	2	-14

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Quadratic twists for elliptic curve 232a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29
464a1	1856b1	2088m1	5800g1	11368c1	28072f1	39208e1	67048a1	83752c1	122728a1	6728d1

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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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