Cremona's table of elliptic curves

7770 = 2 · 3 · 5 · 7 · 37

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 7- 37-	Signs for the Atkin-Lehner involutions
Class	7770t	Isogeny class
Conductor	7770	Conductor
∏ cp	210	Product of Tamagawa factors cp
deg	10080	Modular degree for the optimal curve
Δ	-89547696000 = -1 · 27 · 32 · 53 · 75 · 37	Discriminant
Eigenvalues	2- 3+ 5- 7- -4  1 -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1705,29975]	[a1,a2,a3,a4,a6]
Generators	[-37:228:1]	Generators of the group modulo torsion
j	-548166867106321/89547696000	j-invariant
L	5.6686435680109	L(r)(E,1)/r!
Ω	1.0348557759108	Real period
R	0.02608435052343	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	62160ct1 23310o1 38850bc1 54390cw1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 7770t1

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	1	-6	0	-3	3	7	-	-6	-2	-3	-9	10	-6	-3	-13	-9	4	-6	-9	12

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Quadratic twists for elliptic curve 7770t1

-4	-3	5	-7
62160ct1	23310o1	38850bc1	54390cw1

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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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