Cremona's table of elliptic curves

6510 = 2 · 3 · 5 · 7 · 31

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 7- 31-	Signs for the Atkin-Lehner involutions
Class	6510k	Isogeny class
Conductor	6510	Conductor
∏ cp	72	Product of Tamagawa factors cp
Δ	986300590768920 = 23 · 34 · 5 · 73 · 316	Discriminant
Eigenvalues	2+ 3- 5- 7-  0 -4 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-67588,-6597814]	[a1,a2,a3,a4,a6]
Generators	[-138:394:1]	Generators of the group modulo torsion
j	34144696869398652601/986300590768920	j-invariant
L	3.8080620519223	L(r)(E,1)/r!
Ω	0.29661955500638	Real period
R	0.71323349831073	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	52080bg4 19530bx4 32550br4 45570c4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6510k4

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

---

Quadratic twists for elliptic curve 6510k4

-4	-3	5	-7
52080bg4	19530bx4	32550br4	45570c4

---

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