Cremona's table of elliptic curves

3705 = 3 · 5 · 13 · 19

Field	Data	Notes
Atkin-Lehner	3+ 5+ 13+ 19-	Signs for the Atkin-Lehner involutions
Class	3705b	Isogeny class
Conductor	3705	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	25200	Modular degree for the optimal curve
Δ	-1911280609996875 = -1 · 33 · 55 · 137 · 192	Discriminant
Eigenvalues	-2 3+ 5+ -1  3 13+ -5 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-4766,-2105614]	[a1,a2,a3,a4,a6]
j	-11975039274594304/1911280609996875	j-invariant
L	0.41633533721121	L(r)(E,1)/r!
Ω	0.20816766860561	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	59280bq1 11115i1 18525r1 48165j1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3705b1

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	+	+	-1	3	+	-5	-	-7	4	2	5	5	6	-6	-3	4	5	12	-7	-2	-17	-6	-17	-9

---

Quadratic twists for elliptic curve 3705b1

-4	-3	5	13	-19
59280bq1	11115i1	18525r1	48165j1	70395o1

---

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