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	1275f	Isogeny class
Conductor	1275	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	-56376675 = -1 · 33 · 52 · 174	Discriminant
Eigenvalues	2 3- 5+ -1  2  7 17+  3	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-108,-601]	[a1,a2,a3,a4,a6]
j	-5624320000/2255067	j-invariant
L	4.3534192990154	L(r)(E,1)/r!
Ω	0.72556988316923	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	20400bu1 81600f1 3825j1 1275d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1275f1

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
2	-	+	-1	2	7	+	3	6	6	-7	-2	4	-1	-6	-8	-10	-5	-5	4	14	-8	14	-12	-5

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Quadratic twists for elliptic curve 1275f1

-4	8	-3	5	-7	17
20400bu1	81600f1	3825j1	1275d1	62475ba1	21675f1

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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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