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	1232d	Isogeny class
Conductor	1232	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	384997945773056 = 210 · 710 · 113	Discriminant
Eigenvalues	2+ -2  2 7+ 11-  0  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-22792,-936540]	[a1,a2,a3,a4,a6]
j	1278763167594532/375974556419	j-invariant
L	1.1919887670861	L(r)(E,1)/r!
Ω	0.39732958902871	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	616b2 4928u2 11088m2 30800n2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1232d2

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

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Quadratic twists for elliptic curve 1232d2

-4	8	-3	5	-7	-11
616b2	4928u2	11088m2	30800n2	8624i2	13552h2

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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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