Cremona's table of elliptic curves

318 = 2 · 3 · 53

Field	Data	Notes
Atkin-Lehner	2+ 3- 53+	Signs for the Atkin-Lehner involutions
Class	318b	Isogeny class
Conductor	318	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	-228675072 = -1 · 29 · 3 · 533	Discriminant
Eigenvalues	2+ 3-  0  5 -3 -4  6  5	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,44,722]	[a1,a2,a3,a4,a6]
j	9731810375/228675072	j-invariant
L	1.3236964836554	L(r)(E,1)/r!
Ω	1.3236964836554	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2544c2 10176d2 954k2 7950bi2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 318b2

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	5	-3	-4	6	5	-3	3	8	-4	-3	-4	6	+	-12	-1	-13	-15	2	-16	0	0	5

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Quadratic twists for elliptic curve 318b2

-4	8	-3	5	-7	-11	13	17	-19	53
2544c2	10176d2	954k2	7950bi2	15582c2	38478i2	53742r2	91902a2	114798q2	16854l2

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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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