Cremona's table of elliptic curves

19600 = 2⁴ · 5² · 7²

Field	Data	Notes
Atkin-Lehner	2- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	19600cn	Isogeny class
Conductor	19600	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	5184	Modular degree for the optimal curve
Δ	40140800 = 215 · 52 · 72	Discriminant
Eigenvalues	2-  2 5+ 7-  0  2 -3  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-128,512]	[a1,a2,a3,a4,a6]
Generators	[16:48:1]	Generators of the group modulo torsion
j	46585/8	j-invariant
L	7.3828939486403	L(r)(E,1)/r!
Ω	1.947106924485	Real period
R	0.94793124298927	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	2450x1 78400ij1 19600dy1 19600bv1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 19600cn1

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	2	-3	8	-9	-6	5	-8	3	-10	3	-6	12	4	2	9	-10	-5	6	-3	5

---

Quadratic twists for elliptic curve 19600cn1

-4	8	5	-7
2450x1	78400ij1	19600dy1	19600bv1

---

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