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	64	Product of Tamagawa factors cp
Δ	146526652944 = 24 · 34 · 76 · 312	Discriminant
Eigenvalues	2- 3- -2 7+  0  2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2079,-31671]	[a1,a2,a3,a4,a6]
j	993802845830257/146526652944	j-invariant
L	2.8559851079466	L(r)(E,1)/r!
Ω	0.71399627698664	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	10416z2 41664j2 3906g2 32550m2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1302o2

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 1302o2

-4	8	-3	5	-7	-31
10416z2	41664j2	3906g2	32550m2	9114s2	40362w2

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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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