Cremona's table of elliptic curves

3770 = 2 · 5 · 13 · 29

Field	Data	Notes
Atkin-Lehner	2+ 5+ 13+ 29-	Signs for the Atkin-Lehner involutions
Class	3770a	Isogeny class
Conductor	3770	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	19200	Modular degree for the optimal curve
Δ	77694817850000 = 24 · 55 · 133 · 294	Discriminant
Eigenvalues	2+  0 5+  0  4 13+  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-144155,21098325]	[a1,a2,a3,a4,a6]
j	331294738083389475849/77694817850000	j-invariant
L	1.1905862138262	L(r)(E,1)/r!
Ω	0.59529310691311	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	30160t1 120640bh1 33930bd1 18850x1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3770a1

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

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Quadratic twists for elliptic curve 3770a1

-4	8	-3	5	13	29
30160t1	120640bh1	33930bd1	18850x1	49010r1	109330p1

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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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