Cremona's table of elliptic curves

350 = 2 · 5² · 7

Field	Data	Notes
Atkin-Lehner	2- 5- 7+	Signs for the Atkin-Lehner involutions
Class	350f	Isogeny class
Conductor	350	Conductor
∏ cp	66	Product of Tamagawa factors cp
deg	264	Modular degree for the optimal curve
Δ	-62720000 = -1 · 211 · 54 · 72	Discriminant
Eigenvalues	2- -3 5- 7+ -5 -6 -1 -3	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-180,1047]	[a1,a2,a3,a4,a6]
Generators	[-1:35:1]	Generators of the group modulo torsion
j	-1026590625/100352	j-invariant
L	1.6277461855433	L(r)(E,1)/r!
Ω	1.9197624983313	Real period
R	0.01284680840183	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	2800bg1 11200bk1 3150r1 350e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 350f1

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
-	-3	-	+	-5	-6	-1	-3	0	-6	-4	8	11	-8	2	4	4	-2	9	-10	-7	-2	11	-11	-10

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Quadratic twists for elliptic curve 350f1

-4	8	-3	5	-7	-11	13	17	-19
2800bg1	11200bk1	3150r1	350e1	2450bh1	42350bq1	59150bc1	101150cv1	126350bi1

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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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