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	1275b	Isogeny class
Conductor	1275	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	320	Modular degree for the optimal curve
Δ	-8778375 = -1 · 35 · 53 · 172	Discriminant
Eigenvalues	-1 3+ 5-  4  6 -4 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-3,-144]	[a1,a2,a3,a4,a6]
j	-24389/70227	j-invariant
L	1.0505430896622	L(r)(E,1)/r!
Ω	1.0505430896622	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	20400du1 81600ep1 3825o1 1275g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1275b1

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 1275b1

-4	8	-3	5	-7	17
20400du1	81600ep1	3825o1	1275g1	62475cv1	21675x1

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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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