Cremona's table of elliptic curves

657 = 3² · 73

Field	Data	Notes
Atkin-Lehner	3- 73-	Signs for the Atkin-Lehner involutions
Class	657d	Isogeny class
Conductor	657	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	53217 = 36 · 73	Discriminant
Eigenvalues	-1 3- -2  2  2 -6 -2  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-11,10]	[a1,a2,a3,a4,a6]
Generators	[-2:5:1]	Generators of the group modulo torsion
j	185193/73	j-invariant
L	1.3989934744435	L(r)(E,1)/r!
Ω	3.2248295381831	Real period
R	0.43381935630364	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	10512w1 42048z1 73a2 16425f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 657d1

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

---

Quadratic twists for elliptic curve 657d1

-4	8	-3	5	-7	-11	13	73
10512w1	42048z1	73a2	16425f1	32193f1	79497i1	111033d1	47961d1

---

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