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	1300a	Isogeny class
Conductor	1300	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	720	Modular degree for the optimal curve
Δ	-32500000000 = -1 · 28 · 510 · 13	Discriminant
Eigenvalues	2-  0 5+  3  3 13+  1  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,625,-6250]	[a1,a2,a3,a4,a6]
j	10800/13	j-invariant
L	1.8810203760746	L(r)(E,1)/r!
Ω	0.62700679202488	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	5200o1 20800u1 11700k1 1300f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1300a1

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	+	3	3	+	1	4	-2	7	5	-6	4	-6	13	-9	5	13	5	0	2	-14	9	4	2

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Quadratic twists for elliptic curve 1300a1

-4	8	-3	5	-7	13
5200o1	20800u1	11700k1	1300f1	63700r1	16900b1

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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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