Cremona's table of elliptic curves

5037 = 3 · 23 · 73

Field	Data	Notes
Atkin-Lehner	3+ 23+ 73+	Signs for the Atkin-Lehner involutions
Class	5037b	Isogeny class
Conductor	5037	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4992	Modular degree for the optimal curve
Δ	253366137 = 38 · 232 · 73	Discriminant
Eigenvalues	1 3+  0  2  6 -2 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-9970,-387353]	[a1,a2,a3,a4,a6]
Generators	[5394202:116300161:10648]	Generators of the group modulo torsion
j	109616832370851625/253366137	j-invariant
L	4.1820936851449	L(r)(E,1)/r!
Ω	0.47777140529232	Real period
R	8.7533360908993	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	80592w1 15111h1 125925y1 115851c1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 5037b1

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	2	6	-2	-4	-4	+	-6	4	2	10	6	0	-12	4	-10	12	-8	+	-4	-2	-14	-14

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Quadratic twists for elliptic curve 5037b1

-4	-3	5	-23
80592w1	15111h1	125925y1	115851c1

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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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