Cremona's table of elliptic curves

231 = 3 · 7 · 11

Field	Data	Notes
Atkin-Lehner	3+ 7- 11+	Signs for the Atkin-Lehner involutions
Class	231a	Isogeny class
Conductor	231	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-190238433 = -1 · 3 · 78 · 11	Discriminant
Eigenvalues	-1 3+ -2 7- 11+  6  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,126,432]	[a1,a2,a3,a4,a6]
j	221115865823/190238433	j-invariant
L	0.5822888619653	L(r)(E,1)/r!
Ω	1.1645777239306	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	3696w4 14784bm4 693d4 5775n4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 231a4

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	-	+	6	2	4	0	-2	8	6	10	-4	-8	6	4	-10	-12	0	2	16	4	18	2

---

Quadratic twists for elliptic curve 231a4

-4	8	-3	5	-7	-11	13	17	-19	-23
3696w4	14784bm4	693d4	5775n4	1617g4	2541b4	39039h3	66759g3	83391r3	122199f3

---

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