Cremona's table of elliptic curves

2303 = 7² · 47

Field	Data	Notes
Atkin-Lehner	7- 47+	Signs for the Atkin-Lehner involutions
Class	2303a	Isogeny class
Conductor	2303	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8640	Modular degree for the optimal curve
Δ	-223135390967321 = -1 · 715 · 47	Discriminant
Eigenvalues	-1  1 -3 7-  3  6 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,12053,508066]	[a1,a2,a3,a4,a6]
j	1645957774943/1896619529	j-invariant
L	0.74609939918863	L(r)(E,1)/r!
Ω	0.37304969959431	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	36848u1 20727r1 57575h1 329a1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2303a1

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
-1	1	-3	-	3	6	-6	-8	4	2	-6	9	5	-9	+	-1	-3	4	4	0	13	8	-7	4	6

---

Quadratic twists for elliptic curve 2303a1

-4	-3	5	-7	-47
36848u1	20727r1	57575h1	329a1	108241b1

---

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