Cremona's table of elliptic curves

656 = 2⁴ · 41

Field	Data	Notes
Atkin-Lehner	2+ 41-	Signs for the Atkin-Lehner involutions
Class	656b	Isogeny class
Conductor	656	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-1721344 = -1 · 210 · 412	Discriminant
Eigenvalues	2+ -2  2  2 -2  6 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,8,-60]	[a1,a2,a3,a4,a6]
j	48668/1681	j-invariant
L	1.2777975495193	L(r)(E,1)/r!
Ω	1.2777975495193	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	328b2 2624h2 5904e2 16400j2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 656b2

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

---

Quadratic twists for elliptic curve 656b2

-4	8	-3	5	-7	-11	13	41
328b2	2624h2	5904e2	16400j2	32144d2	79376g2	110864c2	26896b2

---

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