Cremona's table of elliptic curves

48841 = 13² · 17²

Field	Data	Notes
Atkin-Lehner	13+ 17+	Signs for the Atkin-Lehner involutions
Class	48841a	Isogeny class
Conductor	48841	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	165888	Modular degree for the optimal curve
Δ	1980626399884457 = 136 · 177	Discriminant
Eigenvalues	1  0 -2  4  0 13+ 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-33578,1020319]	[a1,a2,a3,a4,a6]
Generators	[1254:43301:1]	Generators of the group modulo torsion
j	35937/17	j-invariant
L	6.0677282647231	L(r)(E,1)/r!
Ω	0.41627138414254	Real period
R	3.6440940308831	Regulator
r	1	Rank of the group of rational points
S	0.99999999999967	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	289a1 2873a1	Quadratic twists by: 13 17

Hecke Eigenvalues for elliptic curve 48841a1

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
1	0	-2	4	0	+	+	4	-4	-6	4	-2	-6	4	0	6	12	10	-4	-4	-6	-12	4	-10	2

---

Quadratic twists for elliptic curve 48841a1

13	17
289a1	2873a1

---

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