Cremona's table of elliptic curves

1001 = 7 · 11 · 13

Field	Data	Notes
Atkin-Lehner	7+ 11- 13+	Signs for the Atkin-Lehner involutions
Class	1001c	Isogeny class
Conductor	1001	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	1008	Modular degree for the optimal curve
Δ	-11022011 = -1 · 72 · 113 · 132	Discriminant
Eigenvalues	-2 -3 -3 7+ 11- 13+ -8 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-199,1092]	[a1,a2,a3,a4,a6]
Generators	[-13:38:1] [-6:45:1]	Generators of the group modulo torsion
j	-871531204608/11022011	j-invariant
L	0.98602644955373	L(r)(E,1)/r!
Ω	2.2817875350929	Real period
R	0.03601074575616	Regulator
r	2	Rank of the group of rational points
S	1.0000000000041	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	16016k1 64064c1 9009e1 25025m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1001c1

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	-3	+	-	+	-8	-4	-9	-8	3	-7	0	2	-8	6	-7	-4	-9	-5	-10	12	-6	-9	1

---

Quadratic twists for elliptic curve 1001c1

-4	8	-3	5	-7	-11	13
16016k1	64064c1	9009e1	25025m1	7007d1	11011s1	13013m1

---

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