Cremona's table of elliptic curves

5151 = 3 · 17 · 101

Field	Data	Notes
Atkin-Lehner	3+ 17- 101-	Signs for the Atkin-Lehner involutions
Class	5151a	Isogeny class
Conductor	5151	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	126420993 = 36 · 17 · 1012	Discriminant
Eigenvalues	1 3+  2  0  0  2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-224,1083]	[a1,a2,a3,a4,a6]
Generators	[-2:271:8]	Generators of the group modulo torsion
j	1251680967433/126420993	j-invariant
L	4.4012913525407	L(r)(E,1)/r!
Ω	1.8018263386693	Real period
R	2.4426834362913	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	82416q1 15453c1 128775d1 87567c1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 5151a1

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	0	2	-	-4	-2	-4	10	-10	-4	0	-4	6	4	-4	4	-6	16	10	-4	-6	-6

---

Quadratic twists for elliptic curve 5151a1

-4	-3	5	17
82416q1	15453c1	128775d1	87567c1

---

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