Cremona's table of elliptic curves

651 = 3 · 7 · 31

Field	Data	Notes
Atkin-Lehner	3- 7- 31+	Signs for the Atkin-Lehner involutions
Class	651d	Isogeny class
Conductor	651	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	523636407 = 34 · 7 · 314	Discriminant
Eigenvalues	-1 3- -2 7-  0 -6  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-3044,-64887]	[a1,a2,a3,a4,a6]
Generators	[-32:19:1]	Generators of the group modulo torsion
j	3119367718264897/523636407	j-invariant
L	1.5714303035313	L(r)(E,1)/r!
Ω	0.64274990960696	Real period
R	1.2224274792137	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	10416u4 41664s4 1953d4 16275a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 651d3

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

---

Quadratic twists for elliptic curve 651d3

-4	8	-3	5	-7	-11	13	-31
10416u4	41664s4	1953d4	16275a3	4557e4	78771m4	110019s4	20181i4

---

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