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	3575d	Isogeny class
Conductor	3575	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	560	Modular degree for the optimal curve
Δ	-29046875 = -1 · 56 · 11 · 132	Discriminant
Eigenvalues	0  1 5+  2 11+ 13-  4  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-33,-281]	[a1,a2,a3,a4,a6]
j	-262144/1859	j-invariant
L	1.7619528425739	L(r)(E,1)/r!
Ω	0.88097642128693	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	57200bx1 32175t1 143a1 39325a1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 3575d1

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	1	+	2	+	-	4	2	-7	-2	-3	11	10	4	4	-2	-1	-2	1	-9	16	8	0	-7	13

---

Quadratic twists for elliptic curve 3575d1

-4	-3	5	-11	13
57200bx1	32175t1	143a1	39325a1	46475c1

---

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