Cremona's table of elliptic curves

400 = 2⁴ · 5²

Field	Data	Notes
Atkin-Lehner	2- 5-	Signs for the Atkin-Lehner involutions
Class	400c	Isogeny class
Conductor	400	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-5120000 = -1 · 213 · 54	Discriminant
Eigenvalues	2- -1 5- -2  3 -4 -3 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-8,112]	[a1,a2,a3,a4,a6]
Generators	[12:-40:1]	Generators of the group modulo torsion
j	-25/2	j-invariant
L	1.5552187610293	L(r)(E,1)/r!
Ω	1.9969667382808	Real period
R	0.064899209853981	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	50a1 1600v1 3600bo1 400b3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 400c1

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
-	-1	-	-2	3	-4	-3	-5	-6	0	-2	2	-3	4	-12	6	0	2	13	-12	11	10	9	15	2

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Quadratic twists for elliptic curve 400c1

-4	8	-3	5	-7	-11	13	17
50a1	1600v1	3600bo1	400b3	19600dt1	48400cy1	67600da1	115600cr1

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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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