Cremona's table of elliptic curves

17472 = 2⁶ · 3 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 13-	Signs for the Atkin-Lehner involutions
Class	17472bv	Isogeny class
Conductor	17472	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	13418496 = 214 · 32 · 7 · 13	Discriminant
Eigenvalues	2- 3+  2 7+  0 13-  4  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1937,-32175]	[a1,a2,a3,a4,a6]
Generators	[2208:15965:27]	Generators of the group modulo torsion
j	49081386832/819	j-invariant
L	4.9428130685695	L(r)(E,1)/r!
Ω	0.71961283658924	Real period
R	6.8687116422173	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	17472bj2 4368v2 52416fl2 122304hi2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17472bv2

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	+	0	-	4	0	6	6	-8	2	-10	-12	-6	14	-10	-14	-4	12	-6	-8	6	-14	-18

---

Quadratic twists for elliptic curve 17472bv2

-4	8	-3	-7
17472bj2	4368v2	52416fl2	122304hi2

---

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