Cremona's table of elliptic curves

34656 = 2⁵ · 3 · 19²

Field	Data	Notes
Atkin-Lehner	2- 3- 19+	Signs for the Atkin-Lehner involutions
Class	34656z	Isogeny class
Conductor	34656	Conductor
∏ cp	42	Product of Tamagawa factors cp
deg	24192	Modular degree for the optimal curve
Δ	-18240769728 = -1 · 26 · 37 · 194	Discriminant
Eigenvalues	2- 3-  0  3 -6  3 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,602,3356]	[a1,a2,a3,a4,a6]
Generators	[44:-342:1]	Generators of the group modulo torsion
j	2888000/2187	j-invariant
L	7.2710117505805	L(r)(E,1)/r!
Ω	0.78453484745139	Real period
R	0.22066493025411	Regulator
r	1	Rank of the group of rational points
S	0.99999999999996	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	34656b1 69312b1 103968h1 34656e1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 34656z1

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
-	-	0	3	-6	3	-2	+	-6	-2	7	5	0	-1	-6	6	0	5	-13	8	-11	15	18	0	-2

---

Quadratic twists for elliptic curve 34656z1

-4	8	-3	-19
34656b1	69312b1	103968h1	34656e1

---

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