Cremona's table of elliptic curves

5757 = 3 · 19 · 101

Field	Data	Notes
Atkin-Lehner	3+ 19- 101-	Signs for the Atkin-Lehner involutions
Class	5757c	Isogeny class
Conductor	5757	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1760	Modular degree for the optimal curve
Δ	-39487263 = -1 · 3 · 194 · 101	Discriminant
Eigenvalues	-1 3+ -2 -4  4 -2 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-114,510]	[a1,a2,a3,a4,a6]
Generators	[12:26:1]	Generators of the group modulo torsion
j	-163936758817/39487263	j-invariant
L	1.2928339971635	L(r)(E,1)/r!
Ω	1.9488780946746	Real period
R	2.6534938243623	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	92112o1 17271j1 109383n1	Quadratic twists by: -4 -3 -19

Hecke Eigenvalues for elliptic curve 5757c1

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	-4	4	-2	-6	-	-4	-2	8	-2	-6	4	12	6	-4	-10	12	8	2	0	-4	18	-6

---

Quadratic twists for elliptic curve 5757c1

-4	-3	-19
92112o1	17271j1	109383n1

---

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