Cremona's table of elliptic curves

400 = 2⁴ · 5²

Field	Data	Notes
Atkin-Lehner	2+ 5+	Signs for the Atkin-Lehner involutions
Class	400h	Isogeny class
Conductor	400	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-51200 = -1 · 211 · 52	Discriminant
Eigenvalues	2+ -3 5+  2 -1 -4 -5 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,5,10]	[a1,a2,a3,a4,a6]
Generators	[1:4:1]	Generators of the group modulo torsion
j	270	j-invariant
L	1.2987503631321	L(r)(E,1)/r!
Ω	2.529210762058	Real period
R	0.12837506294605	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	200e1 1600s1 3600m1 400g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 400h1

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
+	-3	+	2	-1	-4	-5	-1	-2	-8	-10	6	-3	4	4	-6	-8	10	-1	12	-3	-6	-13	-9	14

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Quadratic twists for elliptic curve 400h1

-4	8	-3	5	-7	-11	13	17
200e1	1600s1	3600m1	400g1	19600bb1	48400q1	67600s1	115600n1

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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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