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
deg	1152	Modular degree for the optimal curve
Δ	-8775000000 = -1 · 26 · 33 · 58 · 13	Discriminant
Eigenvalues	2+ 3+ 5+ -2  0 13+  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-150,4500]	[a1,a2,a3,a4,a6]
Generators	[5:60:1]	Generators of the group modulo torsion
j	-24137569/561600	j-invariant
L	1.837296933928	L(r)(E,1)/r!
Ω	1.0930859644134	Real period
R	0.84041740253887	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	15600cc1 62400cx1 5850bn1 390c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1950a1

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 1950a1

-4	8	-3	5	-7	13
15600cc1	62400cx1	5850bn1	390c1	95550ei1	25350bx1

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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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