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	6510c	Isogeny class
Conductor	6510	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	-136710000 = -1 · 24 · 32 · 54 · 72 · 31	Discriminant
Eigenvalues	2+ 3+ 5- 7+  2  4 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-227,1341]	[a1,a2,a3,a4,a6]
Generators	[2:29:1]	Generators of the group modulo torsion
j	-1302528459961/136710000	j-invariant
L	2.7422734406654	L(r)(E,1)/r!
Ω	1.7961625398683	Real period
R	0.19084251701871	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	52080cd1 19530bq1 32550cj1 45570bc1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6510c1

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
+	+	-	+	2	4	-4	-4	6	-6	-	-2	-2	-10	8	-6	-12	0	16	-12	-8	-10	8	-8	14

---

Quadratic twists for elliptic curve 6510c1

-4	-3	5	-7
52080cd1	19530bq1	32550cj1	45570bc1

---

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