Cremona's table of elliptic curves

37296 = 2⁴ · 3² · 7 · 37

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 37+	Signs for the Atkin-Lehner involutions
Class	37296z	Isogeny class
Conductor	37296	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	55296	Modular degree for the optimal curve
Δ	147879796176 = 24 · 39 · 73 · 372	Discriminant
Eigenvalues	2+ 3-  2 7-  4  0 -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-27894,-1793045]	[a1,a2,a3,a4,a6]
Generators	[227:1890:1]	Generators of the group modulo torsion
j	205782571927552/12678309	j-invariant
L	7.4987208338212	L(r)(E,1)/r!
Ω	0.36942260039378	Real period
R	3.3830816098002	Regulator
r	1	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	18648y1 12432s1	Quadratic twists by: -4 -3

Hecke Eigenvalues for elliptic curve 37296z1

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

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Quadratic twists for elliptic curve 37296z1

-4	-3
18648y1	12432s1

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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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