Cremona's table of elliptic curves

3757 = 13 · 17²

Field	Data	Notes
Atkin-Lehner	13+ 17+	Signs for the Atkin-Lehner involutions
Class	3757b	Isogeny class
Conductor	3757	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	15325739097877 = 133 · 178	Discriminant
Eigenvalues	-1  0 -4  2 -6 13+ 17+  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-3386412,2399446130]	[a1,a2,a3,a4,a6]
Generators	[1271:11502:1]	Generators of the group modulo torsion
j	177930109857804849/634933	j-invariant
L	1.474400460737	L(r)(E,1)/r!
Ω	0.46688713387887	Real period
R	3.1579376550555	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	60112p2 33813i2 93925f2 48841b2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3757b2

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

---

Quadratic twists for elliptic curve 3757b2

-4	-3	5	13	17
60112p2	33813i2	93925f2	48841b2	221a2

---

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