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Elliptic curves over $\Q$ of conductor 16096
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Conductor
prime
p-power
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CM field Q(sqrt(-1))
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CM field Q(sqrt(-7))
CM discriminant -3
CM discriminant -4
CM discriminant -7
CM discriminant -8
CM discriminant -11
CM discriminant -12
CM discriminant -16
CM discriminant -19
CM discriminant -27
CM discriminant -28
CM discriminant -43
CM discriminant -67
CM discriminant -163
trivial
order 4
order 8
order 12
ℤ/2ℤ
ℤ/3ℤ
ℤ/4ℤ
ℤ/5ℤ
ℤ/6ℤ
ℤ/7ℤ
ℤ/8ℤ
ℤ/9ℤ
ℤ/10ℤ
ℤ/12ℤ
ℤ/2ℤ⊕ℤ/2ℤ
ℤ/2ℤ⊕ℤ/4ℤ
ℤ/2ℤ⊕ℤ/6ℤ
ℤ/2ℤ⊕ℤ/8ℤ
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✓ LMFDB curve label
Cremona curve label
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Label
Cremona label
Class
Cremona class
Class size
Class degree
Conductor
Discriminant
Rank
Torsion
$\textrm{End}^0(E_{\overline\Q})$
CM
Sato-Tate
Semistable
Potentially good
Nonmax $\ell$
$\ell$-adic images
mod-$\ell$ images
Adelic level
Adelic index
Adelic genus
Regulator
$Ш_{\textrm{an}}$
Ш primes
Integral points
Modular degree
Faltings height
j-invariant
$abc$ quality
Szpiro ratio
Weierstrass coefficients
Weierstrass equation
mod-$m$ images
MW-generators
16096.a1
16096e1
16096.a
16096e
$1$
$1$
\( 2^{5} \cdot 503 \)
\( - 2^{6} \cdot 503^{3} \)
$0$
$\mathsf{trivial}$
$\Q$
$\mathrm{SU}(2)$
$3$
3.3.0.1
3Nn
$6036$
$12$
$1$
$1$
$1$
$0$
$14400$
$0.586911$
$79951586112/127263527$
$0.93466$
$3.07893$
$[0, 0, 0, 359, -3464]$
\(y^2=x^3+359x-3464\)
3.3.0.a.1
,
12.6.0.d.1
, 1006.2.0.?, 3018.6.1.?, 6036.12.1.?
$[]$
16096.b1
16096b1
16096.b
16096b
$1$
$1$
\( 2^{5} \cdot 503 \)
\( - 2^{6} \cdot 503 \)
$0$
$\mathsf{trivial}$
$\Q$
$\mathrm{SU}(2)$
$1006$
$2$
$0$
$1$
$1$
$0$
$4672$
$-0.402276$
$-3796416/503$
$0.64833$
$2.01466$
$[0, 0, 0, -13, -20]$
\(y^2=x^3-13x-20\)
1006.2.0.?
$[]$
16096.c1
16096c1
16096.c
16096c
$1$
$1$
\( 2^{5} \cdot 503 \)
\( - 2^{6} \cdot 503 \)
$2$
$\mathsf{trivial}$
$\Q$
$\mathrm{SU}(2)$
$1006$
$2$
$0$
$1.001772282$
$1$
$8$
$768$
$-0.455431$
$8000/503$
$0.73265$
$1.84022$
$[0, -1, 0, 2, 8]$
\(y^2=x^3-x^2+2x+8\)
1006.2.0.?
$[(2, 4), (-1, 2)]$
16096.d1
16096a1
16096.d
16096a
$1$
$1$
\( 2^{5} \cdot 503 \)
\( - 2^{6} \cdot 503 \)
$1$
$\mathsf{trivial}$
$\Q$
$\mathrm{SU}(2)$
$1006$
$2$
$0$
$1.424117619$
$1$
$2$
$576$
$-0.454292$
$-21952/503$
$0.67979$
$1.84375$
$[0, -1, 0, -2, -8]$
\(y^2=x^3-x^2-2x-8\)
1006.2.0.?
$[(3, 2)]$
16096.e1
16096f1
16096.e
16096f
$1$
$1$
\( 2^{5} \cdot 503 \)
\( - 2^{6} \cdot 503 \)
$1$
$\mathsf{trivial}$
$\Q$
$\mathrm{SU}(2)$
$1006$
$2$
$0$
$1.693795932$
$1$
$2$
$768$
$-0.455431$
$8000/503$
$0.73265$
$1.84022$
$[0, 1, 0, 2, -8]$
\(y^2=x^3+x^2+2x-8\)
1006.2.0.?
$[(6, 16)]$
16096.f1
16096g1
16096.f
16096g
$1$
$1$
\( 2^{5} \cdot 503 \)
\( - 2^{6} \cdot 503 \)
$1$
$\mathsf{trivial}$
$\Q$
$\mathrm{SU}(2)$
$1006$
$2$
$0$
$1.018136754$
$1$
$2$
$576$
$-0.454292$
$-21952/503$
$0.67979$
$1.84375$
$[0, 1, 0, -2, 8]$
\(y^2=x^3+x^2-2x+8\)
1006.2.0.?
$[(2, 4)]$
16096.g1
16096h1
16096.g
16096h
$1$
$1$
\( 2^{5} \cdot 503 \)
\( - 2^{6} \cdot 503^{3} \)
$1$
$\mathsf{trivial}$
$\Q$
$\mathrm{SU}(2)$
$3$
3.3.0.1
3Nn
$6036$
$12$
$1$
$1.344673050$
$1$
$0$
$14400$
$0.586911$
$79951586112/127263527$
$0.93466$
$3.07893$
$[0, 0, 0, 359, 3464]$
\(y^2=x^3+359x+3464\)
3.3.0.a.1
,
12.6.0.d.1
, 1006.2.0.?, 3018.6.1.?, 6036.12.1.?
$[(199/3, 4024/3)]$
16096.h1
16096d1
16096.h
16096d
$1$
$1$
\( 2^{5} \cdot 503 \)
\( - 2^{6} \cdot 503 \)
$0$
$\mathsf{trivial}$
$\Q$
$\mathrm{SU}(2)$
$1006$
$2$
$0$
$1$
$1$
$0$
$4672$
$-0.402276$
$-3796416/503$
$0.64833$
$2.01466$
$[0, 0, 0, -13, 20]$
\(y^2=x^3-13x+20\)
1006.2.0.?
$[]$
Download
displayed columns
for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV