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	1275g	Isogeny class
Conductor	1275	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	1600	Modular degree for the optimal curve
Δ	-137162109375 = -1 · 35 · 59 · 172	Discriminant
Eigenvalues	1 3- 5- -4  6  4 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-76,-17827]	[a1,a2,a3,a4,a6]
j	-24389/70227	j-invariant
L	2.3490857617773	L(r)(E,1)/r!
Ω	0.46981715235546	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	20400ct1 81600cl1 3825m1 1275b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1275g1

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
1	-	-	-4	6	4	-	4	0	0	8	6	-12	-6	4	6	8	10	-2	2	-6	4	-8	-6	-6

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Quadratic twists for elliptic curve 1275g1

-4	8	-3	5	-7	17
20400ct1	81600cl1	3825m1	1275b1	62475bg1	21675k1

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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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