Cremona's table of elliptic curves

13776 = 2⁴ · 3 · 7 · 41

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 41-	Signs for the Atkin-Lehner involutions
Class	13776i	Isogeny class
Conductor	13776	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	104448	Modular degree for the optimal curve
Δ	-7438737867853824 = -1 · 212 · 317 · 73 · 41	Discriminant
Eigenvalues	2- 3+ -1 7-  6  3 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,11304,4119984]	[a1,a2,a3,a4,a6]
j	38996155237031/1816098112269	j-invariant
L	1.901797330187	L(r)(E,1)/r!
Ω	0.31696622169783	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	861b1 55104di1 41328bw1 96432ck1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13776i1

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	-	6	3	-6	-6	9	5	8	-7	-	-2	-3	9	12	6	-13	6	4	11	-2	-4	-9

---

Quadratic twists for elliptic curve 13776i1

-4	8	-3	-7
861b1	55104di1	41328bw1	96432ck1

---

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