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	12432bg	Isogeny class
Conductor	12432	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	1036194768 = 24 · 36 · 74 · 37	Discriminant
Eigenvalues	2- 3+  0 7-  4  2  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-453,3528]	[a1,a2,a3,a4,a6]
Generators	[4:42:1]	Generators of the group modulo torsion
j	643956736000/64762173	j-invariant
L	4.4495378983627	L(r)(E,1)/r!
Ω	1.5122769348555	Real period
R	1.4711385844114	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	3108e1 49728ew1 37296cd1 87024di1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12432bg1

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

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Quadratic twists for elliptic curve 12432bg1

-4	8	-3	-7
3108e1	49728ew1	37296cd1	87024di1

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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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