Cremona's table of elliptic curves

2205 = 3² · 5 · 7²

Field	Data	Notes
Atkin-Lehner	3- 5- 7+	Signs for the Atkin-Lehner involutions
Class	2205i	Isogeny class
Conductor	2205	Conductor
∏ cp	36	Product of Tamagawa factors cp
Δ	-196994059171875 = -1 · 37 · 56 · 78	Discriminant
Eigenvalues	0 3- 5- 7+  0 -1 -6  5	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-90552,10509777]	[a1,a2,a3,a4,a6]
Generators	[-343:1102:1]	Generators of the group modulo torsion
j	-19539165184/46875	j-invariant
L	2.7570866409959	L(r)(E,1)/r!
Ω	0.56681566115942	Real period
R	1.2160420176801	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	35280ev2 735d2 11025q2 2205f2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2205i2

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	-1	-6	5	-6	6	5	-7	-12	-1	-6	0	6	2	-7	-12	11	-13	12	-6	-10

---

Quadratic twists for elliptic curve 2205i2

-4	-3	5	-7
35280ev2	735d2	11025q2	2205f2

---

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