Cremona's table of elliptic curves

101920 = 2⁵ · 5 · 7² · 13

Field	Data	Notes
Atkin-Lehner	2+ 5- 7+ 13-	Signs for the Atkin-Lehner involutions
Class	101920k	Isogeny class
Conductor	101920	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	138240	Modular degree for the optimal curve
Δ	-5193843200000 = -1 · 212 · 55 · 74 · 132	Discriminant
Eigenvalues	2+  1 5- 7+  0 13-  0  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3985,-147617]	[a1,a2,a3,a4,a6]
Generators	[81:260:1]	Generators of the group modulo torsion
j	-711812416/528125	j-invariant
L	8.9465786619506	L(r)(E,1)/r!
Ω	0.29102486019849	Real period
R	1.5370815112055	Regulator
r	1	Rank of the group of rational points
S	1.0000000026496	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	101920bk1 101920b1	Quadratic twists by: -4 -7

Hecke Eigenvalues for elliptic curve 101920k1

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	-	+	0	-	0	6	3	-5	0	-4	-9	5	4	2	-4	-13	7	4	0	16	5	-9	-14

---

Quadratic twists for elliptic curve 101920k1

-4	-7
101920bk1	101920b1

---

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