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Elliptic curves over $\Q$ of conductor 112
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prime
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order 4
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ℤ/2ℤ
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no potential CM
potential CM
CM field Q(sqrt(-1))
CM field Q(sqrt(-3))
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
Bad$\ p$
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Discriminant
Regulator
Analytic order of Ш
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$p\ $div$\ $|Ш|
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✓ LMFDB curve label
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✓ Weierstrass equation
Results (12 matches)
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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
Regulator
$Ш_{\textrm{an}}$
Ш primes
Integral points
Modular degree
Faltings height
j-invariant
Weierstrass coefficients
Weierstrass equation
112.a1
112a2
112.a
112a
$2$
$2$
\( 2^{4} \cdot 7 \)
\( 2^{11} \cdot 7^{2} \)
$1$
$\Z/2\Z$
$\Q$
$\mathrm{SU}(2)$
$2$
8.6.0.6
2B
$0.119959949$
$1$
$15$
$16$
$-0.234669$
$3543122/49$
$[0, 1, 0, -40, 84]$
\(y^2=x^3+x^2-40x+84\)
112.a2
112a1
112.a
112a
$2$
$2$
\( 2^{4} \cdot 7 \)
\( - 2^{10} \cdot 7 \)
$1$
$\Z/2\Z$
$\Q$
$\mathrm{SU}(2)$
$2$
8.6.0.1
2B
$0.239919898$
$1$
$11$
$8$
$-0.581243$
$-4/7$
$[0, 1, 0, 0, 4]$
\(y^2=x^3+x^2+4\)
112.b1
112b3
112.b
112b
$4$
$4$
\( 2^{4} \cdot 7 \)
\( 2^{11} \cdot 7 \)
$0$
$\Z/2\Z$
$\Q$
$\mathrm{SU}(2)$
$2$
8.24.0.101
2B
$1$
$1$
$1$
$16$
$-0.002033$
$1443468546/7$
$[0, 0, 0, -299, -1990]$
\(y^2=x^3-299x-1990\)
112.b2
112b4
112.b
112b
$4$
$4$
\( 2^{4} \cdot 7 \)
\( 2^{11} \cdot 7^{4} \)
$0$
$\Z/4\Z$
$\Q$
$\mathrm{SU}(2)$
$2$
8.24.0.49
2B
$1$
$1$
$3$
$16$
$-0.002033$
$11090466/2401$
$[0, 0, 0, -59, 138]$
\(y^2=x^3-59x+138\)
112.b3
112b2
112.b
112b
$4$
$4$
\( 2^{4} \cdot 7 \)
\( 2^{10} \cdot 7^{2} \)
$0$
$\Z/2\Z\oplus\Z/2\Z$
$\Q$
$\mathrm{SU}(2)$
$2$
8.24.0.2
2Cs
$1$
$1$
$3$
$8$
$-0.348607$
$740772/49$
$[0, 0, 0, -19, -30]$
\(y^2=x^3-19x-30\)
112.b4
112b1
112.b
112b
$4$
$4$
\( 2^{4} \cdot 7 \)
\( - 2^{8} \cdot 7 \)
$0$
$\Z/2\Z$
$\Q$
$\mathrm{SU}(2)$
$2$
8.24.0.60
2B
$1$
$1$
$1$
$4$
$-0.695180$
$432/7$
$[0, 0, 0, 1, -2]$
\(y^2=x^3+x-2\)
112.c1
112c6
112.c
112c
$6$
$18$
\( 2^{4} \cdot 7 \)
\( 2^{21} \cdot 7^{2} \)
$0$
$\Z/2\Z$
$\Q$
$\mathrm{SU}(2)$
$2, 3$
8.6.0.6
,
9.12.0.1
2B
,
3B
$1$
$1$
$1$
$144$
$1.106249$
$2251439055699625/25088$
$[0, -1, 0, -43688, 3529328]$
\(y^2=x^3-x^2-43688x+3529328\)
112.c2
112c5
112.c
112c
$6$
$18$
\( 2^{4} \cdot 7 \)
\( - 2^{30} \cdot 7 \)
$0$
$\Z/2\Z$
$\Q$
$\mathrm{SU}(2)$
$2, 3$
8.6.0.1
,
9.12.0.1
2B
,
3B
$1$
$1$
$1$
$72$
$0.759675$
$-548347731625/1835008$
$[0, -1, 0, -2728, 55920]$
\(y^2=x^3-x^2-2728x+55920\)
112.c3
112c4
112.c
112c
$6$
$18$
\( 2^{4} \cdot 7 \)
\( 2^{15} \cdot 7^{6} \)
$0$
$\Z/2\Z$
$\Q$
$\mathrm{SU}(2)$
$2, 3$
8.6.0.6
,
3.12.0.1
2B
,
3Cs
$1$
$1$
$1$
$48$
$0.556942$
$4956477625/941192$
$[0, -1, 0, -568, 4464]$
\(y^2=x^3-x^2-568x+4464\)
112.c4
112c2
112.c
112c
$6$
$18$
\( 2^{4} \cdot 7 \)
\( 2^{13} \cdot 7^{2} \)
$0$
$\Z/2\Z$
$\Q$
$\mathrm{SU}(2)$
$2, 3$
8.6.0.6
,
9.12.0.1
2B
,
3B
$1$
$1$
$1$
$16$
$0.007636$
$128787625/98$
$[0, -1, 0, -168, -784]$
\(y^2=x^3-x^2-168x-784\)
112.c5
112c1
112.c
112c
$6$
$18$
\( 2^{4} \cdot 7 \)
\( - 2^{14} \cdot 7 \)
$0$
$\Z/2\Z$
$\Q$
$\mathrm{SU}(2)$
$2, 3$
8.6.0.1
,
9.12.0.1
2B
,
3B
$1$
$1$
$1$
$8$
$-0.338938$
$-15625/28$
$[0, -1, 0, -8, -16]$
\(y^2=x^3-x^2-8x-16\)
112.c6
112c3
112.c
112c
$6$
$18$
\( 2^{4} \cdot 7 \)
\( - 2^{18} \cdot 7^{3} \)
$0$
$\Z/2\Z$
$\Q$
$\mathrm{SU}(2)$
$2, 3$
8.6.0.1
,
3.12.0.1
2B
,
3Cs
$1$
$1$
$1$
$24$
$0.210368$
$9938375/21952$
$[0, -1, 0, 72, 368]$
\(y^2=x^3-x^2+72x+368\)
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