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	1305b	Isogeny class
Conductor	1305	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	80	Modular degree for the optimal curve
Δ	-3915 = -1 · 33 · 5 · 29	Discriminant
Eigenvalues	-2 3+ 5- -2  3 -4  2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,3,2]	[a1,a2,a3,a4,a6]
Generators	[0:1:1]	Generators of the group modulo torsion
j	110592/145	j-invariant
L	1.4662007896088	L(r)(E,1)/r!
Ω	2.9664105991334	Real period
R	0.24713382396172	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	20880bp1 83520b1 1305a1 6525b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1305b1

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 1305b1

-4	8	-3	5	-7	29
20880bp1	83520b1	1305a1	6525b1	63945b1	37845b1

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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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