Cremona's table of elliptic curves

9744 = 2⁴ · 3 · 7 · 29

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7- 29+	Signs for the Atkin-Lehner involutions
Class	9744c	Isogeny class
Conductor	9744	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	11550615552 = 211 · 34 · 74 · 29	Discriminant
Eigenvalues	2+ 3+ -2 7- -4 -6 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1384,19600]	[a1,a2,a3,a4,a6]
Generators	[-38:126:1] [-24:196:1]	Generators of the group modulo torsion
j	143256979154/5639949	j-invariant
L	4.7641999203358	L(r)(E,1)/r!
Ω	1.2627548811853	Real period
R	0.47160775136587	Regulator
r	2	Rank of the group of rational points
S	0.99999999999985	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4872f3 38976ca4 29232m4 68208u4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 9744c3

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	-6	-6	4	-8	+	-8	2	-6	-4	-12	2	12	2	-12	-16	6	4	-4	18	-2

---

Quadratic twists for elliptic curve 9744c3

-4	8	-3	-7
4872f3	38976ca4	29232m4	68208u4

---

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