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	3	Product of Tamagawa factors cp
Δ	-230296875 = -1 · 3 · 56 · 173	Discriminant
Eigenvalues	0 3+ 5+  4 -3  1 17- -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-1483,-21507]	[a1,a2,a3,a4,a6]
j	-23100424192/14739	j-invariant
L	1.1538902548331	L(r)(E,1)/r!
Ω	0.38463008494437	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	20400dm2 81600ec2 3825e2 51a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1275a2

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

---

Quadratic twists for elliptic curve 1275a2

-4	8	-3	5	-7	17
20400dm2	81600ec2	3825e2	51a2	62475br2	21675p2

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations