Cremona's table of elliptic curves

75712 = 2⁶ · 7 · 13²

Field	Data	Notes
Atkin-Lehner	2+ 7+ 13+	Signs for the Atkin-Lehner involutions
Class	75712d	Isogeny class
Conductor	75712	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	645120	Modular degree for the optimal curve
Δ	-17278801104388096 = -1 · 214 · 75 · 137	Discriminant
Eigenvalues	2+  0 -3 7+ -2 13+ -4 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-394784,95683744]	[a1,a2,a3,a4,a6]
Generators	[273:2873:1]	Generators of the group modulo torsion
j	-86044336128/218491	j-invariant
L	2.4049747503482	L(r)(E,1)/r!
Ω	0.39053998629153	Real period
R	3.0790377862105	Regulator
r	1	Rank of the group of rational points
S	1.0000000002963	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	75712cm1 4732b1 5824k1	Quadratic twists by: -4 8 13

Hecke Eigenvalues for elliptic curve 75712d1

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
+	0	-3	+	-2	+	-4	-1	-7	-7	5	4	6	-9	7	-11	0	2	-10	0	-7	1	-11	1	13

---

Quadratic twists for elliptic curve 75712d1

-4	8	13
75712cm1	4732b1	5824k1

---

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