Cremona's table of elliptic curves

2208 = 2⁵ · 3 · 23

Field	Data	Notes
Atkin-Lehner	2+ 3+ 23+	Signs for the Atkin-Lehner involutions
Class	2208a	Isogeny class
Conductor	2208	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	-119232 = -1 · 26 · 34 · 23	Discriminant
Eigenvalues	2+ 3+  0  0  2 -2 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,2,16]	[a1,a2,a3,a4,a6]
Generators	[0:4:1]	Generators of the group modulo torsion
j	8000/1863	j-invariant
L	2.6905868861116	L(r)(E,1)/r!
Ω	2.5643461300052	Real period
R	1.0492292185635	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	2208g1 4416x1 6624g1 55200ci1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2208a1

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

---

Quadratic twists for elliptic curve 2208a1

-4	8	-3	5	-7	-23
2208g1	4416x1	6624g1	55200ci1	108192r1	50784a1

---

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