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	8	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	31248 = 24 · 32 · 7 · 31	Discriminant
Eigenvalues	2- 3-  2 7+  4  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-42,-108]	[a1,a2,a3,a4,a6]
j	8205738913/31248	j-invariant
L	3.7511363839677	L(r)(E,1)/r!
Ω	1.8755681919839	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	10416y1 41664l1 3906i1 32550o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1302n1

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 1302n1

-4	8	-3	5	-7	-31
10416y1	41664l1	3906i1	32550o1	9114t1	40362v1

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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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