Cremona's table of elliptic curves

3185 = 5 · 7² · 13

Field	Data	Notes
Atkin-Lehner	5+ 7- 13-	Signs for the Atkin-Lehner involutions
Class	3185d	Isogeny class
Conductor	3185	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	720	Modular degree for the optimal curve
Δ	-1035125 = -1 · 53 · 72 · 132	Discriminant
Eigenvalues	1 -3 5+ 7-  0 13- -4 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,5,-50]	[a1,a2,a3,a4,a6]
Generators	[6:10:1]	Generators of the group modulo torsion
j	251559/21125	j-invariant
L	2.2092825174843	L(r)(E,1)/r!
Ω	1.316755788402	Real period
R	0.83891126089732	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	50960bg1 28665bv1 15925i1 3185e1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3185d1

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	-3	+	-	0	-	-4	-2	9	-5	0	8	9	-1	-4	6	4	13	-3	4	-8	-12	-15	-15	-10

---

Quadratic twists for elliptic curve 3185d1

-4	-3	5	-7	13
50960bg1	28665bv1	15925i1	3185e1	41405p1

---

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