Cremona's table of elliptic curves

1072 = 2⁴ · 67

Field	Data	Notes
Atkin-Lehner	2- 67-	Signs for the Atkin-Lehner involutions
Class	1072b	Isogeny class
Conductor	1072	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	72	Modular degree for the optimal curve
Δ	-17152 = -1 · 28 · 67	Discriminant
Eigenvalues	2- -2  2 -2  4 -6  3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,3,7]	[a1,a2,a3,a4,a6]
Generators	[-1:2:1]	Generators of the group modulo torsion
j	8192/67	j-invariant
L	2.0109287158822	L(r)(E,1)/r!
Ω	2.847189860519	Real period
R	0.3531427151675	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	268a1 4288d1 9648s1 26800s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1072b1

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	-6	3	-1	-3	-1	-2	-5	8	-10	3	-6	-7	-10	-	8	-15	-16	-12	15	-8

---

Quadratic twists for elliptic curve 1072b1

-4	8	-3	5	-7	-11	-67
268a1	4288d1	9648s1	26800s1	52528bs1	129712y1	71824d1

---

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