Cremona's table of elliptic curves

123 = 3 · 41

Field	Data	Notes
Atkin-Lehner	3- 41-	Signs for the Atkin-Lehner involutions
Class	123a	Isogeny class
Conductor	123	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	20	Modular degree for the optimal curve
Δ	-9963 = -1 · 35 · 41	Discriminant
Eigenvalues	-2 3- -4 -2 -3 -6  3  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-10,10]	[a1,a2,a3,a4,a6]
Generators	[-4:1:1]	Generators of the group modulo torsion
j	-122023936/9963	j-invariant
L	0.67159051375054	L(r)(E,1)/r!
Ω	3.9950826935673	Real period
R	0.84052141753148	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	5	Number of elements in the torsion subgroup
Twists	1968j1 7872h1 369b1 3075d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 123a1

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	-	-4	-2	-3	-6	3	0	-6	5	7	-7	-	-1	3	-6	0	-3	-2	-3	-11	10	-16	-10	-12

---

Quadratic twists for elliptic curve 123a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	41
1968j1	7872h1	369b1	3075d1	6027c1	14883j1	20787f1	35547d1	44403c1	65067u1	103443a1	118203e1	5043b1

---

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