Cremona's table of elliptic curves

357 = 3 · 7 · 17

Field	Data	Notes
Atkin-Lehner	3+ 7- 17-	Signs for the Atkin-Lehner involutions
Class	357b	Isogeny class
Conductor	357	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	-122451 = -1 · 3 · 74 · 17	Discriminant
Eigenvalues	0 3+  1 7- -5 -5 17- -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-5,-16]	[a1,a2,a3,a4,a6]
Generators	[4:3:1]	Generators of the group modulo torsion
j	-16777216/122451	j-invariant
L	1.4226357062443	L(r)(E,1)/r!
Ω	1.3908121474417	Real period
R	0.25572031939415	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	5712r1 22848bl1 1071c1 8925p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 357b1

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	-	-5	-5	-	-5	-1	-6	-6	4	7	-7	6	6	14	0	-12	4	6	-6	-6	12	8

---

Quadratic twists for elliptic curve 357b1

-4	8	-3	5	-7	-11	13	17	-19
5712r1	22848bl1	1071c1	8925p1	2499k1	43197a1	60333a1	6069d1	128877s1

---

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