Cremona's table of elliptic curves

400 = 2⁴ · 5²

Field	Data	Notes
Atkin-Lehner	2+ 5-	Signs for the Atkin-Lehner involutions
Class	400d	Isogeny class
Conductor	400	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	2000 = 24 · 53	Discriminant
Eigenvalues	2+  2 5-  2  4 -4  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3,2]	[a1,a2,a3,a4,a6]
j	2048	j-invariant
L	2.0709009523614	L(r)(E,1)/r!
Ω	4.1418019047228	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	200b1 1600x1 3600s1 400f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 400d1

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	4	-4	0	4	-2	2	0	-4	2	-6	-6	4	12	-10	14	-8	-8	-16	2	6	-16

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Quadratic twists for elliptic curve 400d1

-4	8	-3	5	-7	-11	13	17
200b1	1600x1	3600s1	400f1	19600bo1	48400ba1	67600y1	115600y1

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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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