Cremona's table of elliptic curves

3542 = 2 · 7 · 11 · 23

Field	Data	Notes
Atkin-Lehner	2- 7- 11+ 23+	Signs for the Atkin-Lehner involutions
Class	3542p	Isogeny class
Conductor	3542	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-7169008 = -1 · 24 · 7 · 112 · 232	Discriminant
Eigenvalues	2- -2  0 7- 11+ -2 -4  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-13,129]	[a1,a2,a3,a4,a6]
Generators	[-4:13:1]	Generators of the group modulo torsion
j	-244140625/7169008	j-invariant
L	3.7506810682781	L(r)(E,1)/r!
Ω	1.9691204683399	Real period
R	0.47618735478384	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	28336be1 113344br1 31878s1 88550f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3542p1

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	0	-	+	-2	-4	8	+	2	-2	-6	10	-4	-6	-10	-6	-8	-12	0	6	8	4	0	-4

---

Quadratic twists for elliptic curve 3542p1

-4	8	-3	5	-7	-11	-23
28336be1	113344br1	31878s1	88550f1	24794bf1	38962e1	81466bf1

---

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