Cremona's table of elliptic curves

1775 = 5² · 71

Field	Data	Notes
Atkin-Lehner	5+ 71+	Signs for the Atkin-Lehner involutions
Class	1775a	Isogeny class
Conductor	1775	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-27961796875 = -1 · 57 · 713	Discriminant
Eigenvalues	0  2 5+  1  0 -5 -6 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-2383,-44707]	[a1,a2,a3,a4,a6]
Generators	[57:37:1]	Generators of the group modulo torsion
j	-95820414976/1789555	j-invariant
L	3.3175025314738	L(r)(E,1)/r!
Ω	0.34126547880107	Real period
R	2.4302945489307	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	28400v2 113600l2 15975k2 355a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1775a2

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

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Quadratic twists for elliptic curve 1775a2

-4	8	-3	5	-7	-71
28400v2	113600l2	15975k2	355a2	86975d2	126025a2

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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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