Cremona's table of elliptic curves

5200 = 2⁴ · 5² · 13

Field	Data	Notes
Atkin-Lehner	2- 5+ 13-	Signs for the Atkin-Lehner involutions
Class	5200bb	Isogeny class
Conductor	5200	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	4160000000 = 212 · 57 · 13	Discriminant
Eigenvalues	2- -2 5+ -4 -2 13- -2  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-408,-812]	[a1,a2,a3,a4,a6]
Generators	[-12:50:1]	Generators of the group modulo torsion
j	117649/65	j-invariant
L	2.1321853189581	L(r)(E,1)/r!
Ω	1.1370532875778	Real period
R	0.46879626096947	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	325c1 20800cn1 46800ek1 1040c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5200bb1

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	+	-4	-2	-	-2	6	-6	2	10	2	-6	10	4	-2	-6	2	-4	-6	6	12	-16	2	2

---

Quadratic twists for elliptic curve 5200bb1

-4	8	-3	5	13
325c1	20800cn1	46800ek1	1040c1	67600ce1

---

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