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	1232g	Isogeny class
Conductor	1232	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-137984 = -1 · 28 · 72 · 11	Discriminant
Eigenvalues	2-  1 -1 7- 11+ -4 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-21,-49]	[a1,a2,a3,a4,a6]
Generators	[7:14:1]	Generators of the group modulo torsion
j	-4194304/539	j-invariant
L	2.8333455531209	L(r)(E,1)/r!
Ω	1.1028070354323	Real period
R	0.64230310972088	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	308a1 4928bg1 11088bx1 30800bb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1232g1

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	-1	-	+	-4	-6	2	-1	2	1	-9	6	-8	8	10	-1	-2	-11	-11	-14	14	-4	13	-9

---

Quadratic twists for elliptic curve 1232g1

-4	8	-3	5	-7	-11
308a1	4928bg1	11088bx1	30800bb1	8624q1	13552o1

---

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