Cremona's table of elliptic curves

27744 = 2⁵ · 3 · 17²

Field	Data	Notes
Atkin-Lehner	2- 3- 17+	Signs for the Atkin-Lehner involutions
Conductor	27744	Conductor
Count	4	Number of curves in isogeny class
Curves	27744z1 27744z2 27744z3 27744z4	Curves in isogeny class
deg	73728	Modular degree for the optimal curve
Eigenvalues	2- 3- -2  0  4 -2 17+  0	Hecke eigenvalues for primes less than 20
L	6.1328435752529	L(r)(E,1)/r!
r	1	Rank of the group of rational points
Twists	27744r 55488cl 83232j 1632h	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for isogeny class 27744z

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	0	4	-2	+	0	8	6	0	-2	-10	-8	8	-10	0	-10	-8	8	6	-8	0	-6	-10

---

Quadratic twists for isogeny class 27744z

-4	8	-3	17
27744r	55488cl	83232j	1632h

---

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