Cremona's table of elliptic curves

12480 = 2⁶ · 3 · 5 · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 13+	Signs for the Atkin-Lehner involutions
Class	12480cx	Isogeny class
Conductor	12480	Conductor
∏ cp	11	Product of Tamagawa factors cp
deg	84480	Modular degree for the optimal curve
Δ	-5388160292536320 = -1 · 214 · 311 · 5 · 135	Discriminant
Eigenvalues	2- 3- 5-  1 -5 13+  3 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,38875,-1928445]	[a1,a2,a3,a4,a6]
j	396555344454656/328867205355	j-invariant
L	2.611567757395	L(r)(E,1)/r!
Ω	0.23741525067227	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	12480k1 3120b1 37440dx1 62400et1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12480cx1

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	-5	+	3	-6	-7	6	10	11	5	-4	2	5	0	-1	-4	5	6	-11	-8	7	-13

---

Quadratic twists for elliptic curve 12480cx1

-4	8	-3	5
12480k1	3120b1	37440dx1	62400et1

---

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