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	350d	Isogeny class
Conductor	350	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-437500 = -1 · 22 · 56 · 7	Discriminant
Eigenvalues	2-  2 5+ 7+  0  4 -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-13,31]	[a1,a2,a3,a4,a6]
j	-15625/28	j-invariant
L	2.6582491802628	L(r)(E,1)/r!
Ω	2.6582491802628	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2800v1 11200j1 3150l1 14a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 350d1

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	+	+	0	4	-6	2	0	-6	-4	-2	6	-8	12	-6	-6	8	4	0	-2	8	6	-6	10

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Quadratic twists for elliptic curve 350d1

-4	8	-3	5	-7	-11	13	17	-19
2800v1	11200j1	3150l1	14a4	2450y1	42350bb1	59150o1	101150cl1	126350q1

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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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