Cremona's table of elliptic curves

1950 = 2 · 3 · 5² · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 13+	Signs for the Atkin-Lehner involutions
Class	1950a	Isogeny class
Conductor	1950	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-6436523437500 = -1 · 22 · 3 · 512 · 133	Discriminant
Eigenvalues	2+ 3+ 5+ -2  0 13+  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,1350,-120000]	[a1,a2,a3,a4,a6]
Generators	[50:250:1]	Generators of the group modulo torsion
j	17394111071/411937500	j-invariant
L	1.837296933928	L(r)(E,1)/r!
Ω	0.3643619881378	Real period
R	2.5212522076166	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	15600cc3 62400cx3 5850bn3 390c3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1950a3

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

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Quadratic twists for elliptic curve 1950a3

-4	8	-3	5	-7	13
15600cc3	62400cx3	5850bn3	390c3	95550ei3	25350bx3

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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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