Cremona's table of elliptic curves

3721 = 61²

Field	Data	Notes
Atkin-Lehner	61+	Signs for the Atkin-Lehner involutions
Class	3721a	Isogeny class
Conductor	3721	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	7440	Modular degree for the optimal curve
Δ	-3142742836021 = -1 · 617	Discriminant
Eigenvalues	1 -2 -3 -1  5  1 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-7520,264447]	[a1,a2,a3,a4,a6]
Generators	[249:3596:1]	Generators of the group modulo torsion
j	-912673/61	j-invariant
L	2.2586714831481	L(r)(E,1)/r!
Ω	0.78527491474625	Real period
R	1.4381406057508	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	59536g1 33489f1 93025a1 61a1	Quadratic twists by: -4 -3 5 61

Hecke Eigenvalues for elliptic curve 3721a1

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	-3	-1	5	1	-4	-4	9	6	0	-8	5	8	4	-6	-9	+	7	8	-11	-3	4	4	-14

---

Quadratic twists for elliptic curve 3721a1

-4	-3	5	61
59536g1	33489f1	93025a1	61a1

---

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