Cremona's table of elliptic curves

53200 = 2⁴ · 5² · 7 · 19

Field	Data	Notes
Atkin-Lehner	2- 5+ 7- 19+	Signs for the Atkin-Lehner involutions
Class	53200cn	Isogeny class
Conductor	53200	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-6454694873200 = -1 · 24 · 52 · 73 · 196	Discriminant
Eigenvalues	2- -2 5+ 7- -3 -2 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-4758,-177377]	[a1,a2,a3,a4,a6]
Generators	[2682:48013:8]	Generators of the group modulo torsion
j	-29787105760000/16136737183	j-invariant
L	2.7038053498195	L(r)(E,1)/r!
Ω	0.2803222233555	Real period
R	1.6075579722966	Regulator
r	1	Rank of the group of rational points
S	1.0000000000063	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13300h2 53200dg2	Quadratic twists by: -4 5

Hecke Eigenvalues for elliptic curve 53200cn2

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	+	-	-3	-2	-6	+	-3	-9	-2	1	0	-1	-12	6	12	8	-1	-9	4	13	0	-12	10

---

Quadratic twists for elliptic curve 53200cn2

-4	5
13300h2	53200dg2

---

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