Cremona's table of elliptic curves

1952 = 2⁵ · 61

Field	Data	Notes
Atkin-Lehner	2- 61-	Signs for the Atkin-Lehner involutions
Class	1952c	Isogeny class
Conductor	1952	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	-929714176 = -1 · 212 · 613	Discriminant
Eigenvalues	2-  0  1  3 -3 -3  2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-332,2752]	[a1,a2,a3,a4,a6]
Generators	[-3:61:1]	Generators of the group modulo torsion
j	-988047936/226981	j-invariant
L	3.1752600942984	L(r)(E,1)/r!
Ω	1.4998959299216	Real period
R	0.35283115658834	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1952d1 3904f1 17568d1 48800e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1952c1

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	1	3	-3	-3	2	-6	-3	-4	0	-2	-11	0	12	-10	3	-	15	12	-3	-15	0	4	6

---

Quadratic twists for elliptic curve 1952c1

-4	8	-3	5	-7	61
1952d1	3904f1	17568d1	48800e1	95648p1	119072b1

---

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