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	5037c	Isogeny class
Conductor	5037	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	32419859691 = 3 · 236 · 73	Discriminant
Eigenvalues	1 3+  2 -4  2 -2  6  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-914,5805]	[a1,a2,a3,a4,a6]
Generators	[7602:25799:216]	Generators of the group modulo torsion
j	84587175295273/32419859691	j-invariant
L	3.9197792476709	L(r)(E,1)/r!
Ω	1.0653282907323	Real period
R	7.3588194020013	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	80592ba2 15111j2 125925z2 115851d2	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 5037c2

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

---

Quadratic twists for elliptic curve 5037c2

-4	-3	5	-23
80592ba2	15111j2	125925z2	115851d2

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations