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	17472x	Isogeny class
Conductor	17472	Conductor
∏ cp	80	Product of Tamagawa factors cp
deg	15360	Modular degree for the optimal curve
Δ	-348237646848 = -1 · 210 · 35 · 72 · 134	Discriminant
Eigenvalues	2+ 3-  0 7+  2 13-  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1253,32715]	[a1,a2,a3,a4,a6]
Generators	[7:156:1]	Generators of the group modulo torsion
j	-212629504000/340075827	j-invariant
L	6.1373805719025	L(r)(E,1)/r!
Ω	0.85985366480709	Real period
R	0.35688517843786	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	17472cj1 1092a1 52416bv1 122304i1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17472x1

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	+	2	-	4	-4	2	-6	0	-10	4	4	0	-10	-4	2	0	-6	14	-4	-16	12	6

---

Quadratic twists for elliptic curve 17472x1

-4	8	-3	-7
17472cj1	1092a1	52416bv1	122304i1

---

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