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	5037a	Isogeny class
Conductor	5037	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1344	Modular degree for the optimal curve
Δ	347553 = 32 · 232 · 73	Discriminant
Eigenvalues	1 3+  0  2  0 -2 -4  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-805,8464]	[a1,a2,a3,a4,a6]
Generators	[0:92:1]	Generators of the group modulo torsion
j	57803487729625/347553	j-invariant
L	4.0179629887962	L(r)(E,1)/r!
Ω	2.6998357491172	Real period
R	1.4882249744674	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	80592v1 15111g1 125925x1 115851b1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 5037a1

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	0	-2	-4	8	+	0	10	-10	-2	-6	12	0	-8	2	-12	16	+	-4	4	-2	-2

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Quadratic twists for elliptic curve 5037a1

-4	-3	5	-23
80592v1	15111g1	125925x1	115851b1

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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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