Cremona's table of elliptic curves

224 = 2⁵ · 7

Field	Data	Notes
Atkin-Lehner	2+ 7+	Signs for the Atkin-Lehner involutions
Class	224a	Isogeny class
Conductor	224	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	-448 = -1 · 26 · 7	Discriminant
Eigenvalues	2+ -2  0 7+ -4 -4 -2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,2,0]	[a1,a2,a3,a4,a6]
Generators	[1:2:1]	Generators of the group modulo torsion
j	8000/7	j-invariant
L	1.1435250753789	L(r)(E,1)/r!
Ω	2.9056796323957	Real period
R	0.78709645938225	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	224b1 448d1 2016l1 5600u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 224a1

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
+	-2	0	+	-4	-4	-2	-6	8	2	-4	10	-10	4	4	-2	10	-8	-8	0	-6	-16	2	18	-2

---

Quadratic twists for elliptic curve 224a1

-4	8	-3	5	-7	-11	13	17	-19	-23
224b1	448d1	2016l1	5600u1	1568c1	27104x1	37856s1	64736h1	80864i1	118496e1

---

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