Cremona's table of elliptic curves

657 = 3² · 73

Field	Data	Notes
Atkin-Lehner	3- 73+	Signs for the Atkin-Lehner involutions
Class	657a	Isogeny class
Conductor	657	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	944016363 = 311 · 732	Discriminant
Eigenvalues	-1 3-  4  2  4 -2  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-11678,488634]	[a1,a2,a3,a4,a6]
j	241583200934041/1294947	j-invariant
L	1.3920168886714	L(r)(E,1)/r!
Ω	1.3920168886714	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	10512q2 42048o2 219c2 16425k2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 657a2

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

---

Quadratic twists for elliptic curve 657a2

-4	8	-3	5	-7	-11	13	73
10512q2	42048o2	219c2	16425k2	32193i2	79497k2	111033e2	47961g2

---

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