Cremona's table of elliptic curves

3575 = 5² · 11 · 13

Field	Data	Notes
Atkin-Lehner	5- 11+ 13+	Signs for the Atkin-Lehner involutions
Class	3575f	Isogeny class
Conductor	3575	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1680	Modular degree for the optimal curve
Δ	983125 = 54 · 112 · 13	Discriminant
Eigenvalues	-2 -3 5- -4 11+ 13+ -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-25,6]	[a1,a2,a3,a4,a6]
Generators	[-5:2:1] [-1:5:1]	Generators of the group modulo torsion
j	2764800/1573	j-invariant
L	1.4898650005478	L(r)(E,1)/r!
Ω	2.3884429991597	Real period
R	0.10396347474589	Regulator
r	2	Rank of the group of rational points
S	0.99999999999793	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	57200ci1 32175x1 3575e1 39325v1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 3575f1

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	-	-4	+	+	-6	-2	3	-1	-8	10	-6	-9	10	-1	-8	-7	-8	-8	-14	1	-10	2	-6

---

Quadratic twists for elliptic curve 3575f1

-4	-3	5	-11	13
57200ci1	32175x1	3575e1	39325v1	46475k1

---

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