Cremona's table of elliptic curves

1258 = 2 · 17 · 37

Field	Data	Notes
Atkin-Lehner	2+ 17- 37-	Signs for the Atkin-Lehner involutions
Class	1258d	Isogeny class
Conductor	1258	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	336	Modular degree for the optimal curve
Δ	-2576384 = -1 · 212 · 17 · 37	Discriminant
Eigenvalues	2+  0  3 -3  5 -6 17- -5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-43,-123]	[a1,a2,a3,a4,a6]
Generators	[22:85:1]	Generators of the group modulo torsion
j	-8908363017/2576384	j-invariant
L	2.1415511440391	L(r)(E,1)/r!
Ω	0.91745657277854	Real period
R	1.1671130861014	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	10064i1 40256j1 11322s1 31450i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1258d1

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	5	-6	-	-5	-2	-7	-8	-	6	-9	6	13	-7	-5	-2	3	-10	4	-2	12	-9

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Quadratic twists for elliptic curve 1258d1

-4	8	-3	5	-7	17	37
10064i1	40256j1	11322s1	31450i1	61642j1	21386a1	46546c1

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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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