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	1302n	Isogeny class
Conductor	1302	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-976683582 = -1 · 2 · 38 · 74 · 31	Discriminant
Eigenvalues	2- 3-  2 7+  4  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,248,62]	[a1,a2,a3,a4,a6]
j	1686433811327/976683582	j-invariant
L	3.7511363839677	L(r)(E,1)/r!
Ω	0.93778409599193	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10416y4 41664l3 3906i4 32550o3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1302n4

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

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Quadratic twists for elliptic curve 1302n4

-4	8	-3	5	-7	-31
10416y4	41664l3	3906i4	32550o3	9114t4	40362v3

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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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