Cremona's table of elliptic curves

5684 = 2² · 7² · 29

Field	Data	Notes
Atkin-Lehner	2- 7- 29-	Signs for the Atkin-Lehner involutions
Class	5684k	Isogeny class
Conductor	5684	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	25704	Modular degree for the optimal curve
Δ	1763657945052416 = 28 · 710 · 293	Discriminant
Eigenvalues	2-  2  3 7-  0  1  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-70429,6928041]	[a1,a2,a3,a4,a6]
j	534274048/24389	j-invariant
L	4.1926479334543	L(r)(E,1)/r!
Ω	0.46584977038381	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	22736bo1 90944bf1 51156t1 5684c1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5684k1

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	3	-	0	1	0	4	0	-	-2	8	6	2	0	9	0	-8	-4	3	16	8	-3	-12	10

---

Quadratic twists for elliptic curve 5684k1

-4	8	-3	-7
22736bo1	90944bf1	51156t1	5684c1

---

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