Cremona's table of elliptic curves

288 = 2⁵ · 3²

Field	Data	Notes
Atkin-Lehner	2+ 3-	Signs for the Atkin-Lehner involutions
Class	288c	Isogeny class
Conductor	288	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	8957952 = 212 · 37	Discriminant
Eigenvalues	2+ 3- -2  4  4 -2  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-156,-736]	[a1,a2,a3,a4,a6]
j	140608/3	j-invariant
L	1.3526394018325	L(r)(E,1)/r!
Ω	1.3526394018325	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	288b3 576b1 96b3 7200bq2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 288c2

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	4	4	-2	6	4	0	-2	-4	-2	-2	-4	8	-10	-4	6	-4	-16	-6	-4	12	-10	-14

---

Quadratic twists for elliptic curve 288c2

-4	8	-3	5	-7	-11	13	17	-19
288b3	576b1	96b3	7200bq2	14112v3	34848cg3	48672bs3	83232m3	103968cg3

---

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