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	357c	Isogeny class
Conductor	357	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-722211 = -1 · 3 · 72 · 173	Discriminant
Eigenvalues	2 3-  1 7+  1  1 17+  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,20,-17]	[a1,a2,a3,a4,a6]
j	841232384/722211	j-invariant
L	3.1461696978284	L(r)(E,1)/r!
Ω	1.5730848489142	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	5712o1 22848a1 1071b1 8925j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 357c1

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	+	1	1	+	1	-3	-2	0	-6	-1	5	12	0	0	-2	-8	0	6	-4	6	16	-12

---

Quadratic twists for elliptic curve 357c1

-4	8	-3	5	-7	-11	13	17	-19
5712o1	22848a1	1071b1	8925j1	2499f1	43197o1	60333o1	6069c1	128877b1

---

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