Cremona's table of elliptic curves

1305 = 3² · 5 · 29

Field	Data	Notes
Atkin-Lehner	3+ 5+ 29+	Signs for the Atkin-Lehner involutions
Class	1305a	Isogeny class
Conductor	1305	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	-2854035 = -1 · 39 · 5 · 29	Discriminant
Eigenvalues	2 3+ 5+ -2 -3 -4 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,27,-61]	[a1,a2,a3,a4,a6]
Generators	[18:23:8]	Generators of the group modulo torsion
j	110592/145	j-invariant
L	4.3403603690126	L(r)(E,1)/r!
Ω	1.3579630038095	Real period
R	1.5981143657215	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	20880be1 83520p1 1305b1 6525a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1305a1

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
2	+	+	-2	-3	-4	-2	-2	5	+	2	-5	-1	-1	6	3	4	6	2	-12	9	-16	7	-6	-13

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Quadratic twists for elliptic curve 1305a1

-4	8	-3	5	-7	29
20880be1	83520p1	1305b1	6525a1	63945c1	37845a1

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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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