Cremona's table of elliptic curves

296 = 2³ · 37

Field	Data	Notes
Atkin-Lehner	2- 37-	Signs for the Atkin-Lehner involutions
Class	296b	Isogeny class
Conductor	296	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	9472 = 28 · 37	Discriminant
Eigenvalues	2- -1  0 -3 -3  0  2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-33,85]	[a1,a2,a3,a4,a6]
Generators	[3:2:1]	Generators of the group modulo torsion
j	16000000/37	j-invariant
L	1.3782253636796	L(r)(E,1)/r!
Ω	4.103770394291	Real period
R	0.16792184153345	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	592b1 2368a1 2664c1 7400a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 296b1

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	0	-3	-3	0	2	-2	-6	-2	-4	-	7	4	1	9	8	-4	12	-5	-13	-10	-1	-2	-12

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Quadratic twists for elliptic curve 296b1

-4	8	-3	5	-7	-11	13	17	-19	37
592b1	2368a1	2664c1	7400a1	14504i1	35816a1	50024a1	85544b1	106856a1	10952a1

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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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