Cremona's table of elliptic curves

45600 = 2⁵ · 3 · 5² · 19

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 19-	Signs for the Atkin-Lehner involutions
Class	45600z	Isogeny class
Conductor	45600	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	368640	Modular degree for the optimal curve
Δ	-285803727075000000 = -1 · 26 · 35 · 58 · 196	Discriminant
Eigenvalues	2- 3+ 5+  0 -2 -2  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,145342,14329812]	[a1,a2,a3,a4,a6]
Generators	[211:7372:1]	Generators of the group modulo torsion
j	339542483015744/285803727075	j-invariant
L	4.6214172015217	L(r)(E,1)/r!
Ω	0.19972137943047	Real period
R	3.8565535770435	Regulator
r	1	Rank of the group of rational points
S	0.99999999999865	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	45600bp1 91200hh2 9120f1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 45600z1

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

---

Quadratic twists for elliptic curve 45600z1

-4	8	5
45600bp1	91200hh2	9120f1

---

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