Cremona's table of elliptic curves

2626 = 2 · 13 · 101

Field	Data	Notes
Atkin-Lehner	2+ 13+ 101+	Signs for the Atkin-Lehner involutions
Class	2626b	Isogeny class
Conductor	2626	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	312	Modular degree for the optimal curve
Δ	-34138 = -1 · 2 · 132 · 101	Discriminant
Eigenvalues	2+  2 -4  3  0 13+ -3 -1	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-2,-10]	[a1,a2,a3,a4,a6]
Generators	[7:16:1]	Generators of the group modulo torsion
j	-1771561/34138	j-invariant
L	2.8487521302432	L(r)(E,1)/r!
Ω	1.5856677981038	Real period
R	0.89828151068268	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	21008f1 84032o1 23634k1 65650t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2626b1

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	-4	3	0	+	-3	-1	4	-1	-4	4	-6	3	-12	-5	4	-5	-2	-2	-4	6	-4	0	-13

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Quadratic twists for elliptic curve 2626b1

-4	8	-3	5	-7	13
21008f1	84032o1	23634k1	65650t1	128674l1	34138g1

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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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