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	8450w	Isogeny class
Conductor	8450	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	4291015625000 = 23 · 512 · 133	Discriminant
Eigenvalues	2- -2 5+  0  0 13- -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-14713,678417]	[a1,a2,a3,a4,a6]
Generators	[92:279:1]	Generators of the group modulo torsion
j	10260751717/125000	j-invariant
L	4.3991962191853	L(r)(E,1)/r!
Ω	0.78061705283317	Real period
R	0.93925615281289	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	67600ct2 76050by2 1690d2 8450i2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 8450w2

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	+	0	0	-	-6	0	0	6	6	6	0	-10	-12	0	12	10	12	-6	-6	-8	-12	12	-18

---

Quadratic twists for elliptic curve 8450w2

-4	-3	5	13
67600ct2	76050by2	1690d2	8450i2

---

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