Cremona's table of elliptic curves

1221 = 3 · 11 · 37

Field	Data	Notes
Atkin-Lehner	3- 11- 37-	Signs for the Atkin-Lehner involutions
Class	1221c	Isogeny class
Conductor	1221	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	80	Modular degree for the optimal curve
Δ	45177 = 3 · 11 · 372	Discriminant
Eigenvalues	-1 3-  0  0 11-  4  2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-13,-16]	[a1,a2,a3,a4,a6]
j	244140625/45177	j-invariant
L	1.2726912446243	L(r)(E,1)/r!
Ω	2.5453824892487	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	19536s1 78144a1 3663c1 30525h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1221c1

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	-	0	0	-	4	2	-2	-6	2	4	-	6	6	12	2	10	0	4	16	2	-14	12	12	10

---

Quadratic twists for elliptic curve 1221c1

-4	8	-3	5	-7	-11	37
19536s1	78144a1	3663c1	30525h1	59829h1	13431e1	45177j1

---

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