Cremona's table of elliptic curves

3762 = 2 · 3² · 11 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 11+ 19-	Signs for the Atkin-Lehner involutions
Class	3762o	Isogeny class
Conductor	3762	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	46337246208 = 210 · 39 · 112 · 19	Discriminant
Eigenvalues	2- 3-  4  0 11+  4  2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-11543,-474321]	[a1,a2,a3,a4,a6]
j	233301213501481/63562752	j-invariant
L	4.6060634986376	L(r)(E,1)/r!
Ω	0.46060634986376	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	30096bi1 120384bo1 1254c1 94050s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3762o1

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

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Quadratic twists for elliptic curve 3762o1

-4	8	-3	5	-11	-19
30096bi1	120384bo1	1254c1	94050s1	41382z1	71478s1

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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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