Cremona's table of elliptic curves

99 = 3² · 11

Field	Data	Notes
Atkin-Lehner	3- 11+	Signs for the Atkin-Lehner involutions
Class	99b	Isogeny class
Conductor	99	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	64304361 = 312 · 112	Discriminant
Eigenvalues	-1 3-  2  4 11+ -2  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-104,-102]	[a1,a2,a3,a4,a6]
j	169112377/88209	j-invariant
L	0.79230740387988	L(r)(E,1)/r!
Ω	1.5846148077598	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1584q2 6336bd2 33a1 2475g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 99b2

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	-	2	4	+	-2	2	0	-8	6	-8	6	2	0	-8	-6	4	6	-4	0	-14	-4	-12	6	2

---

Quadratic twists for elliptic curve 99b2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
1584q2	6336bd2	33a1	2475g2	4851j2	1089g2	16731k2	28611u2	35739q2	52371e2	83259l2	95139j2

---

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