Cremona's table of elliptic curves

1300 = 2² · 5² · 13

Field	Data	Notes
Atkin-Lehner	2- 5+ 13-	Signs for the Atkin-Lehner involutions
Class	1300b	Isogeny class
Conductor	1300	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	-676000000 = -1 · 28 · 56 · 132	Discriminant
Eigenvalues	2-  0 5+  2 -2 13- -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,25,-1250]	[a1,a2,a3,a4,a6]
Generators	[15:50:1]	Generators of the group modulo torsion
j	432/169	j-invariant
L	2.6693841005024	L(r)(E,1)/r!
Ω	0.75622317134652	Real period
R	0.58831488764296	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5200v2 20800c2 11700o2 52a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1300b2

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	+	2	-2	-	-6	-6	-8	2	10	6	-6	-4	2	-6	-10	-2	-10	10	-2	-4	6	-6	-2

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Quadratic twists for elliptic curve 1300b2

-4	8	-3	5	-7	13
5200v2	20800c2	11700o2	52a1	63700j2	16900a2

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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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