Cremona's table of elliptic curves

101568 = 2⁶ · 3 · 23²

Field	Data	Notes
Atkin-Lehner	2+ 3- 23-	Signs for the Atkin-Lehner involutions
Class	101568t	Isogeny class
Conductor	101568	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	21504	Modular degree for the optimal curve
Δ	-2742336 = -1 · 26 · 34 · 232	Discriminant
Eigenvalues	2+ 3-  1  2  4  3 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-360,-2754]	[a1,a2,a3,a4,a6]
Generators	[125:1386:1]	Generators of the group modulo torsion
j	-152827456/81	j-invariant
L	10.770766045269	L(r)(E,1)/r!
Ω	0.5478726779889	Real period
R	4.9148125434085	Regulator
r	1	Rank of the group of rational points
S	1.0000000005001	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	101568f1 50784t1 101568w1	Quadratic twists by: -4 8 -23

Hecke Eigenvalues for elliptic curve 101568t1

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
+	-	1	2	4	3	-6	-2	-	-5	2	-10	3	6	0	-3	-6	-3	4	-6	-1	8	-6	-3	-7

---

Quadratic twists for elliptic curve 101568t1

-4	8	-23
101568f1	50784t1	101568w1

---

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