Cremona's table of elliptic curves

1295 = 5 · 7 · 37

Field	Data	Notes
Atkin-Lehner	5- 7+ 37-	Signs for the Atkin-Lehner involutions
Class	1295a	Isogeny class
Conductor	1295	Conductor
∏ cp	28	Product of Tamagawa factors cp
deg	4480	Modular degree for the optimal curve
Δ	-2460861244296875 = -1 · 57 · 75 · 374	Discriminant
Eigenvalues	0 -1 5- 7+  5 -1  1  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,18965,-2171027]	[a1,a2,a3,a4,a6]
Generators	[89:462:1]	Generators of the group modulo torsion
j	754326479523774464/2460861244296875	j-invariant
L	2.0319269017422	L(r)(E,1)/r!
Ω	0.2339420065852	Real period
R	0.31020003195935	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	20720q1 82880b1 11655e1 6475b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1295a1

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	-	+	5	-1	1	2	-6	-1	-8	-	0	-6	-1	-12	-8	0	-4	0	-10	11	-4	-12	5

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Quadratic twists for elliptic curve 1295a1

-4	8	-3	5	-7	37
20720q1	82880b1	11655e1	6475b1	9065a1	47915a1

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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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