Cremona's table of elliptic curves

8450 = 2 · 5² · 13²

Field	Data	Notes
Atkin-Lehner	2+ 5+ 13+	Signs for the Atkin-Lehner involutions
Class	8450a	Isogeny class
Conductor	8450	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	40320	Modular degree for the optimal curve
Δ	-1115664062500000 = -1 · 25 · 513 · 134	Discriminant
Eigenvalues	2+  0 5+  3 -3 13+  4  7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-21917,2040741]	[a1,a2,a3,a4,a6]
Generators	[149:1363:1]	Generators of the group modulo torsion
j	-2609064081/2500000	j-invariant
L	3.3214535340886	L(r)(E,1)/r!
Ω	0.44623873489584	Real period
R	3.7216105128838	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	67600bi1 76050et1 1690g1 8450n1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 8450a1

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
+	0	+	3	-3	+	4	7	4	-8	-10	-3	-2	-6	1	9	-4	-14	-4	6	-4	10	0	1	-16

---

Quadratic twists for elliptic curve 8450a1

-4	-3	5	13
67600bi1	76050et1	1690g1	8450n1

---

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