Cremona's table of elliptic curves

5313 = 3 · 7 · 11 · 23

Field	Data	Notes
Atkin-Lehner	3+ 7+ 11- 23-	Signs for the Atkin-Lehner involutions
Class	5313a	Isogeny class
Conductor	5313	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	-218558899251 = -1 · 32 · 73 · 11 · 235	Discriminant
Eigenvalues	2 3+ -3 7+ 11-  2  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-162,-22453]	[a1,a2,a3,a4,a6]
Generators	[330:1583:8]	Generators of the group modulo torsion
j	-473093337088/218558899251	j-invariant
L	5.2994066067575	L(r)(E,1)/r!
Ω	0.44756401075535	Real period
R	1.1840555718083	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	85008ch1 15939e1 37191j1 58443m1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 5313a1

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	+	-3	+	-	2	6	2	-	2	-2	-4	1	-7	4	-10	-6	6	-4	-9	-9	-13	4	1	-2

---

Quadratic twists for elliptic curve 5313a1

-4	-3	-7	-11	-23
85008ch1	15939e1	37191j1	58443m1	122199h1

---

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