Cremona's table of elliptic curves

1232 = 2⁴ · 7 · 11

Field	Data	Notes
Atkin-Lehner	2- 7- 11+	Signs for the Atkin-Lehner involutions
Class	1232i	Isogeny class
Conductor	1232	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	5300793344 = 212 · 76 · 11	Discriminant
Eigenvalues	2- -2 -2 7- 11+  4  4  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-824,-8684]	[a1,a2,a3,a4,a6]
Generators	[-20:14:1]	Generators of the group modulo torsion
j	15124197817/1294139	j-invariant
L	1.8155421392618	L(r)(E,1)/r!
Ω	0.89584978384627	Real period
R	0.67553815829366	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	77c2 4928bh2 11088by2 30800bd2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1232i2

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

---

Quadratic twists for elliptic curve 1232i2

-4	8	-3	5	-7	-11
77c2	4928bh2	11088by2	30800bd2	8624s2	13552s2

---

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