Cremona's table of elliptic curves

5698 = 2 · 7 · 11 · 37

Field	Data	Notes
Atkin-Lehner	2- 7- 11+ 37+	Signs for the Atkin-Lehner involutions
Class	5698c	Isogeny class
Conductor	5698	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	3328	Modular degree for the optimal curve
Δ	-296843008 = -1 · 28 · 7 · 112 · 372	Discriminant
Eigenvalues	2-  2 -2 7- 11+  4 -4 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,141,-463]	[a1,a2,a3,a4,a6]
Generators	[21:100:1]	Generators of the group modulo torsion
j	309876419663/296843008	j-invariant
L	7.104017297171	L(r)(E,1)/r!
Ω	0.94330754229315	Real period
R	0.9413707855952	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	45584j1 51282p1 39886m1 62678b1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 5698c1

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

---

Quadratic twists for elliptic curve 5698c1

-4	-3	-7	-11
45584j1	51282p1	39886m1	62678b1

---

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