Cremona's table of elliptic curves

850 = 2 · 5² · 17

Field	Data	Notes
Atkin-Lehner	2+ 5+ 17-	Signs for the Atkin-Lehner involutions
Class	850a	Isogeny class
Conductor	850	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-19191406250000000 = -1 · 27 · 515 · 173	Discriminant
Eigenvalues	2+ -1 5+ -2  0  1 17- -1	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-166025,-26946875]	[a1,a2,a3,a4,a6]
j	-32391289681150609/1228250000000	j-invariant
L	0.7079651961325	L(r)(E,1)/r!
Ω	0.11799419935542	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	6800r2 27200u2 7650bv2 170c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 850a2

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	+	-2	0	1	-	-1	6	-3	5	-8	6	10	3	3	3	11	-2	9	-11	8	12	15	7

---

Quadratic twists for elliptic curve 850a2

-4	8	-3	5	-7	-11	17
6800r2	27200u2	7650bv2	170c2	41650g2	102850cb2	14450c2

---

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