Cremona's table of elliptic curves

64 = 2⁶

Field	Data	Notes
Atkin-Lehner	2-	Signs for the Atkin-Lehner involutions
Class	64a	Isogeny class
Conductor	64	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2	Modular degree for the optimal curve
Δ	4096 = 212	Discriminant
Eigenvalues	2-  0  2  0  0 -6  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4,0]	[a1,a2,a3,a4,a6]
j	1728	j-invariant
L	0.92703733865069	L(r)(E,1)/r!
Ω	3.7081493546027	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	64a1 32a2 576h2 1600o2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 64a1

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
-	0	2	0	0	-6	2	0	0	10	0	2	10	0	0	-14	0	10	0	0	-6	0	0	10	18

---

Quadratic twists for elliptic curve 64a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43
64a1	32a2	576h2	1600o2	3136t2	7744t2	10816bb2	18496i2	23104bo2	33856ba2	53824r2	61504bn2	87616z2	107584h2	118336bd2

---

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