Cremona's table of elliptic curves

1275 = 3 · 5² · 17

Field	Data	Notes
Atkin-Lehner	3+ 5+ 17-	Signs for the Atkin-Lehner involutions
Class	1275a	Isogeny class
Conductor	1275	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	216	Modular degree for the optimal curve
Δ	-7171875 = -1 · 33 · 56 · 17	Discriminant
Eigenvalues	0 3+ 5+  4 -3  1 17- -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,17,-132]	[a1,a2,a3,a4,a6]
j	32768/459	j-invariant
L	1.1538902548331	L(r)(E,1)/r!
Ω	1.1538902548331	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	20400dm1 81600ec1 3825e1 51a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1275a1

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	+	+	4	-3	1	-	-1	-9	6	2	4	-3	7	6	6	6	8	4	12	-2	-10	6	0	16

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Quadratic twists for elliptic curve 1275a1

-4	8	-3	5	-7	17
20400dm1	81600ec1	3825e1	51a1	62475br1	21675p1

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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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