Cremona's table of elliptic curves

24720 = 2⁴ · 3 · 5 · 103

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 103-	Signs for the Atkin-Lehner involutions
Class	24720r	Isogeny class
Conductor	24720	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4512	Modular degree for the optimal curve
Δ	123600 = 24 · 3 · 52 · 103	Discriminant
Eigenvalues	2- 3- 5+  0 -4  2 -8 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-101,-426]	[a1,a2,a3,a4,a6]
j	7192182784/7725	j-invariant
L	0.75241853250467	L(r)(E,1)/r!
Ω	1.5048370650095	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	6180a1 98880bl1 74160bt1 123600s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 24720r1

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

---

Quadratic twists for elliptic curve 24720r1

-4	8	-3	5
6180a1	98880bl1	74160bt1	123600s1

---

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