Cremona's table of elliptic curves

13328 = 2⁴ · 7² · 17

Field	Data	Notes
Atkin-Lehner	2+ 7- 17+	Signs for the Atkin-Lehner involutions
Class	13328d	Isogeny class
Conductor	13328	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-34816574464 = -1 · 210 · 76 · 172	Discriminant
Eigenvalues	2+ -2  2 7-  6 -2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,768,3940]	[a1,a2,a3,a4,a6]
j	415292/289	j-invariant
L	1.4691877742075	L(r)(E,1)/r!
Ω	0.73459388710375	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6664d2 53312bv2 119952bo2 272c2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13328d2

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

---

Quadratic twists for elliptic curve 13328d2

-4	8	-3	-7
6664d2	53312bv2	119952bo2	272c2

---

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