Cremona's table of elliptic curves

1411 = 17 · 83

Field	Data	Notes
Atkin-Lehner	17+ 83+	Signs for the Atkin-Lehner involutions
Class	1411b	Isogeny class
Conductor	1411	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	108	Modular degree for the optimal curve
Δ	117113 = 17 · 832	Discriminant
Eigenvalues	-1 -2  0 -2 -2  2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-28,-57]	[a1,a2,a3,a4,a6]
Generators	[-3:3:1]	Generators of the group modulo torsion
j	2433138625/117113	j-invariant
L	1.1588152690293	L(r)(E,1)/r!
Ω	2.0812467751673	Real period
R	1.1135779599574	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	22576d1 90304e1 12699b1 35275e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1411b1

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	-2	0	-2	-2	2	+	4	2	6	2	6	-6	4	8	-6	4	-2	-12	12	-16	8	+	-18	0

---

Quadratic twists for elliptic curve 1411b1

-4	8	-3	5	-7	17	-83
22576d1	90304e1	12699b1	35275e1	69139b1	23987c1	117113b1

---

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