Cremona's table of elliptic curves

12432 = 2⁴ · 3 · 7 · 37

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 37+	Signs for the Atkin-Lehner involutions
Class	12432z	Isogeny class
Conductor	12432	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	22609133568 = 218 · 32 · 7 · 372	Discriminant
Eigenvalues	2- 3+  2 7+ -2  4 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-38192,2885568]	[a1,a2,a3,a4,a6]
j	1504154129818033/5519808	j-invariant
L	2.111423787392	L(r)(E,1)/r!
Ω	1.055711893696	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	1554m2 49728ek2 37296bq2 87024ds2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12432z2

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

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Quadratic twists for elliptic curve 12432z2

-4	8	-3	-7
1554m2	49728ek2	37296bq2	87024ds2

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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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