Cremona's table of elliptic curves

99 = 3² · 11

Field	Data	Notes
Atkin-Lehner	3+ 11+	Signs for the Atkin-Lehner involutions
Class	99a	Isogeny class
Conductor	99	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	3267 = 33 · 112	Discriminant
Eigenvalues	-1 3+ -4 -2 11+ -2  2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-17,30]	[a1,a2,a3,a4,a6]
Generators	[0:5:1]	Generators of the group modulo torsion
j	19034163/121	j-invariant
L	0.68055155913983	L(r)(E,1)/r!
Ω	4.4984528865883	Real period
R	0.15128569228075	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	1584k2 6336j2 99c2 2475a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 99a2

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
-1	+	-4	-2	+	-2	2	-6	4	-6	4	-6	-10	6	-8	0	4	-6	8	0	-2	-10	12	0	2

---

Quadratic twists for elliptic curve 99a2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
1584k2	6336j2	99c2	2475a2	4851d2	1089c2	16731d2	28611e2	35739e2	52371b2	83259d2	95139b2

---

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