Cremona's table of elliptic curves

34 = 2 · 17

Field	Data	Notes
Atkin-Lehner	2- 17+	Signs for the Atkin-Lehner involutions
Class	34a	Isogeny class
Conductor	34	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	2	Modular degree for the optimal curve
Δ	1088 = 26 · 17	Discriminant
Eigenvalues	2- -2  0 -4  6  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-3,1]	[a1,a2,a3,a4,a6]
j	3048625/1088	j-invariant
L	0.74927722105228	L(r)(E,1)/r!
Ω	4.4956633263137	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	272d1 1088c1 306b1 850b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 34a1

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	6	2	+	-4	0	0	-4	-4	6	8	0	-6	0	-4	8	0	2	8	0	-6	14

---

Quadratic twists for elliptic curve 34a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61
272d1	1088c1	306b1	850b1	1666l1	4114b1	5746e1	578a1	12274d1	17986j1	28594f1	32674d1	46546a1	57154n1	62866c1	75106b1	95506a1	118354e1	126514e1

---

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