Cremona's table of elliptic curves

65 = 5 · 13

Field	Data	Notes
Atkin-Lehner	5+ 13+	Signs for the Atkin-Lehner involutions
Conductor	65	Conductor
Count	2	Number of curves in isogeny class
Curves	65a1 65a2	Curves in isogeny class
deg	2	Modular degree for the optimal curve
Eigenvalues	-1 -2 5+ -4  2 13+  2 -6	Hecke eigenvalues for primes less than 20
L	0.50533434230686	L(r)(E,1)/r!
r	1	Rank of the group of rational points
Twists	1040c 4160g 585h 325c	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for isogeny class 65a

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	+	-4	2	+	2	-6	-6	2	-10	-2	-6	10	4	2	6	2	-4	6	-6	-12	-16	2	-2

---

Quadratic twists for isogeny class 65a

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43
1040c	4160g	585h	325c	3185i	7865b	845a	18785c	23465a	34385i	54665c	62465h	88985f	109265e	120185d

---

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