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	1275c	Isogeny class
Conductor	1275	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-541875 = -1 · 3 · 54 · 172	Discriminant
Eigenvalues	0 3+ 5- -1  2  1 17- -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,17,18]	[a1,a2,a3,a4,a6]
Generators	[12:42:1]	Generators of the group modulo torsion
j	819200/867	j-invariant
L	1.9581895746819	L(r)(E,1)/r!
Ω	1.9349876089758	Real period
R	0.16866512612264	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	20400dv1 81600et1 3825k1 1275e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1275c1

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	+	-	-1	2	1	-	-1	-4	-4	7	-6	2	-3	-4	-14	6	-7	-11	2	-2	0	-4	10	-9

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Quadratic twists for elliptic curve 1275c1

-4	8	-3	5	-7	17
20400dv1	81600et1	3825k1	1275e1	62475cm1	21675v1

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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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