Cremona's table of elliptic curves

5700 = 2² · 3 · 5² · 19

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 19-	Signs for the Atkin-Lehner involutions
Class	5700f	Isogeny class
Conductor	5700	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	13824	Modular degree for the optimal curve
Δ	328961250000 = 24 · 36 · 57 · 192	Discriminant
Eigenvalues	2- 3+ 5+ -2  0  4 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-30533,2063562]	[a1,a2,a3,a4,a6]
Generators	[98:54:1]	Generators of the group modulo torsion
j	12592337649664/1315845	j-invariant
L	3.1425994571849	L(r)(E,1)/r!
Ω	0.92396168184553	Real period
R	1.7006113559319	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	22800cv1 91200cz1 17100z1 1140c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5700f1

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	0	4	-6	-	-6	6	8	4	-6	10	-6	-12	12	-10	4	0	-14	8	18	-6	-8

---

Quadratic twists for elliptic curve 5700f1

-4	8	-3	5	-19
22800cv1	91200cz1	17100z1	1140c1	108300cd1

---

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