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	1258a	Isogeny class
Conductor	1258	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	300	Modular degree for the optimal curve
Δ	-5816992 = -1 · 25 · 173 · 37	Discriminant
Eigenvalues	2+  2  2  3  2  3 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-164,752]	[a1,a2,a3,a4,a6]
j	-492477523273/5816992	j-invariant
L	2.4074183882636	L(r)(E,1)/r!
Ω	2.4074183882636	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	10064b1 40256a1 11322y1 31450r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1258a1

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	2	3	+	-4	6	0	-2	-	0	-2	-4	0	2	4	-15	0	-14	6	-1	8	-9

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Quadratic twists for elliptic curve 1258a1

-4	8	-3	5	-7	17	37
10064b1	40256a1	11322y1	31450r1	61642m1	21386b1	46546g1

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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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