Cremona's table of elliptic curves

1885 = 5 · 13 · 29

Field	Data	Notes
Atkin-Lehner	5+ 13+ 29+	Signs for the Atkin-Lehner involutions
Class	1885a	Isogeny class
Conductor	1885	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	400	Modular degree for the optimal curve
Δ	1885 = 5 · 13 · 29	Discriminant
Eigenvalues	0 -1 5+  1  0 13+  5  7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-2211,-39288]	[a1,a2,a3,a4,a6]
Generators	[-9198:-169:343]	Generators of the group modulo torsion
j	1195876549033984/1885	j-invariant
L	2.0079211790384	L(r)(E,1)/r!
Ω	0.69620317832175	Real period
R	2.8841022873217	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	30160o1 120640bo1 16965n1 9425d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1885a1

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	+	1	0	+	5	7	-2	+	-7	4	-5	-4	-8	-2	6	-4	5	-8	-2	10	-1	-2	-6

---

Quadratic twists for elliptic curve 1885a1

-4	8	-3	5	-7	13	29
30160o1	120640bo1	16965n1	9425d1	92365k1	24505b1	54665a1

---

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