Cremona's table of elliptic curves

5865 = 3 · 5 · 17 · 23

Field	Data	Notes
Atkin-Lehner	3+ 5+ 17- 23-	Signs for the Atkin-Lehner involutions
Class	5865a	Isogeny class
Conductor	5865	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	3168	Modular degree for the optimal curve
Δ	139616325 = 33 · 52 · 17 · 233	Discriminant
Eigenvalues	-2 3+ 5+  1  2  5 17-  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-276,1766]	[a1,a2,a3,a4,a6]
Generators	[-7:57:1]	Generators of the group modulo torsion
j	2333584543744/139616325	j-invariant
L	1.7976637166829	L(r)(E,1)/r!
Ω	1.8103203787277	Real period
R	0.1655014344244	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	93840cd1 17595q1 29325o1 99705s1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 5865a1

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	+	+	1	2	5	-	0	-	3	-10	-1	10	-8	-6	-1	-4	-5	-4	-11	-14	1	-11	15	11

---

Quadratic twists for elliptic curve 5865a1

-4	-3	5	17
93840cd1	17595q1	29325o1	99705s1

---

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