Cremona's table of elliptic curves

1072 = 2⁴ · 67

Field	Data	Notes
Atkin-Lehner	2- 67+	Signs for the Atkin-Lehner involutions
Class	1072a	Isogeny class
Conductor	1072	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	200	Modular degree for the optimal curve
Δ	-274432 = -1 · 212 · 67	Discriminant
Eigenvalues	2-  2  2  2  4  2  3 -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-197,1133]	[a1,a2,a3,a4,a6]
j	-207474688/67	j-invariant
L	3.0299684014551	L(r)(E,1)/r!
Ω	3.0299684014551	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	67a1 4288f1 9648k1 26800be1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1072a1

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	4	2	3	-7	-9	-5	10	-1	0	2	1	10	-9	-2	+	0	-7	8	-4	7	0

---

Quadratic twists for elliptic curve 1072a1

-4	8	-3	5	-7	-11	-67
67a1	4288f1	9648k1	26800be1	52528bd1	129712m1	71824e1

---

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