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	24	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-169996288 = -1 · 212 · 73 · 112	Discriminant
Eigenvalues	2- -2 -2 7- 11+  4  4  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,56,-588]	[a1,a2,a3,a4,a6]
Generators	[14:56:1]	Generators of the group modulo torsion
j	4657463/41503	j-invariant
L	1.8155421392618	L(r)(E,1)/r!
Ω	0.89584978384627	Real period
R	0.33776907914683	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	77c1 4928bh1 11088by1 30800bd1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1232i1

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

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Quadratic twists for elliptic curve 1232i1

-4	8	-3	5	-7	-11
77c1	4928bh1	11088by1	30800bd1	8624s1	13552s1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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