Cremona's table of elliptic curves

2226 = 2 · 3 · 7 · 53

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7- 53-	Signs for the Atkin-Lehner involutions
Class	2226c	Isogeny class
Conductor	2226	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	-101932992 = -1 · 26 · 34 · 7 · 532	Discriminant
Eigenvalues	2+ 3+  2 7-  4  0 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-129,693]	[a1,a2,a3,a4,a6]
Generators	[-6:39:1]	Generators of the group modulo torsion
j	-240293820313/101932992	j-invariant
L	2.3499349354471	L(r)(E,1)/r!
Ω	1.7695523891586	Real period
R	0.6639913431906	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	17808t1 71232bn1 6678p1 55650cv1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2226c1

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	-	4	0	-6	-8	-4	-6	-6	2	-4	4	-4	-	-6	-10	4	-12	8	8	-12	14	10

---

Quadratic twists for elliptic curve 2226c1

-4	8	-3	5	-7	53
17808t1	71232bn1	6678p1	55650cv1	15582m1	117978x1

---

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