Cremona's table of elliptic curves

1302 = 2 · 3 · 7 · 31

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 31-	Signs for the Atkin-Lehner involutions
Class	1302o	Isogeny class
Conductor	1302	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-15446876516316 = -1 · 22 · 32 · 712 · 31	Discriminant
Eigenvalues	2- 3- -2 7+  0  2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,3501,-171171]	[a1,a2,a3,a4,a6]
j	4745612697439823/15446876516316	j-invariant
L	2.8559851079466	L(r)(E,1)/r!
Ω	0.35699813849332	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10416z4 41664j3 3906g4 32550m3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1302o4

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

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Quadratic twists for elliptic curve 1302o4

-4	8	-3	5	-7	-31
10416z4	41664j3	3906g4	32550m3	9114s4	40362w3

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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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