Cremona's table of elliptic curves

50400 = 2⁵ · 3² · 5² · 7

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7+	Signs for the Atkin-Lehner involutions
Class	50400dj	Isogeny class
Conductor	50400	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	-612360000000000 = -1 · 212 · 37 · 510 · 7	Discriminant
Eigenvalues	2- 3- 5+ 7+ -4 -6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,17700,-772000]	[a1,a2,a3,a4,a6]
Generators	[70:900:1]	Generators of the group modulo torsion
j	13144256/13125	j-invariant
L	4.2571461937742	L(r)(E,1)/r!
Ω	0.27987697490522	Real period
R	0.95067354932985	Regulator
r	1	Rank of the group of rational points
S	1.0000000000077	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	50400bp2 100800eb1 16800d4 10080bc4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 50400dj2

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
-	-	+	+	-4	-6	-2	-4	0	6	8	-6	-6	8	4	-2	0	10	-8	0	10	-4	-4	10	18

---

Quadratic twists for elliptic curve 50400dj2

-4	8	-3	5
50400bp2	100800eb1	16800d4	10080bc4

---

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