Cremona's table of elliptic curves

438 = 2 · 3 · 73

Field	Data	Notes
Atkin-Lehner	2+ 3+ 73+	Signs for the Atkin-Lehner involutions
Class	438c	Isogeny class
Conductor	438	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	10512 = 24 · 32 · 73	Discriminant
Eigenvalues	2+ 3+  0 -2  4 -6  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-5,-3]	[a1,a2,a3,a4,a6]
Generators	[-2:3:1]	Generators of the group modulo torsion
j	18609625/10512	j-invariant
L	1.2587504610108	L(r)(E,1)/r!
Ω	3.3565130070238	Real period
R	0.37501730467803	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	3504t1 14016r1 1314d1 10950bd1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 438c1

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	-2	4	-6	0	-4	0	-4	2	-10	-2	2	-12	0	-4	-6	8	8	+	8	8	10	14

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Quadratic twists for elliptic curve 438c1

-4	8	-3	5	-7	-11	13	17	73
3504t1	14016r1	1314d1	10950bd1	21462s1	52998n1	74022n1	126582u1	31974a1

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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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