Cremona's table of elliptic curves

3718 = 2 · 11 · 13²

Field	Data	Notes
Atkin-Lehner	2+ 11- 13+	Signs for the Atkin-Lehner involutions
Class	3718j	Isogeny class
Conductor	3718	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	-658864340992 = -1 · 221 · 11 · 134	Discriminant
Eigenvalues	2+ -2  0  2 11- 13+  0 -7	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-8961,-329548]	[a1,a2,a3,a4,a6]
j	-2785800837625/23068672	j-invariant
L	0.73568659706582	L(r)(E,1)/r!
Ω	0.24522886568861	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	29744p2 118976j2 33462ce2 92950ci2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3718j2

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	-	+	0	-7	-3	3	8	2	6	5	3	6	-6	2	-4	-15	-16	8	-9	15	-1

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Quadratic twists for elliptic curve 3718j2

-4	8	-3	5	-11	13
29744p2	118976j2	33462ce2	92950ci2	40898bu2	3718n2

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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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