Cremona's table of elliptic curves

117117 = 3² · 7 · 11 · 13²

Field	Data	Notes
Atkin-Lehner	3- 7+ 11+ 13+	Signs for the Atkin-Lehner involutions
Conductor	117117	Conductor
Count	6	Number of curves in isogeny class
Curves	117117r1 117117r2 117117r3 117117r4 117117r5 117117r6	Curves in isogeny class
deg	307200	Modular degree for the optimal curve
Eigenvalues	-1 3- -2 7+ 11+ 13+ -2 -4	Hecke eigenvalues for primes less than 20
L	6.0905332519406	L(r)(E,1)/r!
r	2	Rank of the group of rational points
Twists	39039h 693d	Quadratic twists by: -3 13

Hecke Eigenvalues for isogeny class 117117r

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	-4	0	2	-8	-6	10	-4	-8	-6	4	-10	12	0	-2	16	4	18	-2

---

Quadratic twists for isogeny class 117117r

-3	13
39039h	693d

---

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