Cremona's table of elliptic curves

13680 = 2⁴ · 3² · 5 · 19

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 19-	Signs for the Atkin-Lehner involutions
Class	13680w	Isogeny class
Conductor	13680	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	46080	Modular degree for the optimal curve
Δ	39214330675200 = 222 · 39 · 52 · 19	Discriminant
Eigenvalues	2- 3+ 5+  4 -6  0 -4 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-8883,-114318]	[a1,a2,a3,a4,a6]
Generators	[-33:378:1]	Generators of the group modulo torsion
j	961504803/486400	j-invariant
L	4.6733185672993	L(r)(E,1)/r!
Ω	0.51871866753372	Real period
R	2.2523377602347	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	1710a1 54720dd1 13680y1 68400do1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13680w1

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
-	+	+	4	-6	0	-4	-	-4	10	2	-4	-10	12	0	6	4	-10	8	0	6	10	14	-10	-6

---

Quadratic twists for elliptic curve 13680w1

-4	8	-3	5
1710a1	54720dd1	13680y1	68400do1

---

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