Cremona's table of elliptic curves

6240 = 2⁵ · 3 · 5 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 13-	Signs for the Atkin-Lehner involutions
Class	6240z	Isogeny class
Conductor	6240	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	-13689000000000000 = -1 · 212 · 34 · 512 · 132	Discriminant
Eigenvalues	2- 3+ 5-  4  0 13-  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,52175,-3280223]	[a1,a2,a3,a4,a6]
j	3834800837445824/3342041015625	j-invariant
L	2.6232221058514	L(r)(E,1)/r!
Ω	0.21860184215428	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	6240bf4 12480co1 18720j4 31200p2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6240z4

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

---

Quadratic twists for elliptic curve 6240z4

-4	8	-3	5	13
6240bf4	12480co1	18720j4	31200p2	81120f2

---

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