Cremona's table of elliptic curves

86700 = 2² · 3 · 5² · 17²

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 17+	Signs for the Atkin-Lehner involutions
Class	86700t	Isogeny class
Conductor	86700	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	829440	Modular degree for the optimal curve
Δ	-65171436300000000 = -1 · 28 · 33 · 58 · 176	Discriminant
Eigenvalues	2- 3+ 5-  1 -6  5 17+  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-96333,-16799463]	[a1,a2,a3,a4,a6]
Generators	[543389:21155378:343]	Generators of the group modulo torsion
j	-40960/27	j-invariant
L	6.0149944697433	L(r)(E,1)/r!
Ω	0.1316092202682	Real period
R	7.6172404603361	Regulator
r	1	Rank of the group of rational points
S	1.0000000007086	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	86700bj1 300b1	Quadratic twists by: 5 17

Hecke Eigenvalues for elliptic curve 86700t1

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	-6	5	+	5	6	6	1	-2	0	-1	6	-12	-6	13	11	0	-2	-8	-6	0	7

---

Quadratic twists for elliptic curve 86700t1

5	17
86700bj1	300b1

---

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