Cremona's table of elliptic curves

385 = 5 · 7 · 11

Field	Data	Notes
Atkin-Lehner	5- 7+ 11-	Signs for the Atkin-Lehner involutions
Class	385a	Isogeny class
Conductor	385	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	-2562175 = -1 · 52 · 7 · 114	Discriminant
Eigenvalues	-1  0 5- 7+ 11- -6  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-37,124]	[a1,a2,a3,a4,a6]
Generators	[2:6:1]	Generators of the group modulo torsion
j	-5461074081/2562175	j-invariant
L	1.255102798703	L(r)(E,1)/r!
Ω	2.3974795613599	Real period
R	1.0470185597671	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	6160n1 24640a1 3465f1 1925e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 385a1

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

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Quadratic twists for elliptic curve 385a1

-4	8	-3	5	-7	-11	13	17
6160n1	24640a1	3465f1	1925e1	2695c1	4235g1	65065h1	111265e1

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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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