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Elliptic curves over $\Q$ of conductor 21
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CM discriminant -3
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CM discriminant -19
CM discriminant -27
CM discriminant -28
CM discriminant -43
CM discriminant -67
CM discriminant -163
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✓ LMFDB curve label
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✓ Weierstrass equation
Results (6 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
21.a1
21a5
21.a
21a
$6$
$8$
\( 3 \cdot 7 \)
\( 3 \cdot 7^{2} \)
$0$
$\Z/2\Z$
$\Q$
$\mathrm{SU}(2)$
✓
$2$
16.48.0.48
2B
$1$
$1$
$0$
$4$
$0.074205$
$53297461115137/147$
$[1, 0, 0, -784, -8515]$
\(y^2+xy=x^3-784x-8515\)
21.a2
21a2
21.a
21a
$6$
$8$
\( 3 \cdot 7 \)
\( 3^{2} \cdot 7^{4} \)
$0$
$\Z/2\Z\oplus\Z/2\Z$
$\Q$
$\mathrm{SU}(2)$
✓
$2$
8.48.0.34
2Cs
$1$
$1$
$2$
$2$
$-0.272368$
$13027640977/21609$
$[1, 0, 0, -49, -136]$
\(y^2+xy=x^3-49x-136\)
21.a3
21a3
21.a
21a
$6$
$8$
\( 3 \cdot 7 \)
\( 3^{8} \cdot 7 \)
$0$
$\Z/8\Z$
$\Q$
$\mathrm{SU}(2)$
✓
$2$
8.48.0.159
2B
$1$
$1$
$6$
$2$
$-0.272368$
$6570725617/45927$
$[1, 0, 0, -39, 90]$
\(y^2+xy=x^3-39x+90\)
21.a4
21a6
21.a
21a
$6$
$8$
\( 3 \cdot 7 \)
\( - 3 \cdot 7^{8} \)
$0$
$\Z/2\Z$
$\Q$
$\mathrm{SU}(2)$
✓
$2$
8.48.0.177
2B
$1$
$1$
$0$
$4$
$0.074205$
$-4354703137/17294403$
$[1, 0, 0, -34, -217]$
\(y^2+xy=x^3-34x-217\)
21.a5
21a1
21.a
21a
$6$
$8$
\( 3 \cdot 7 \)
\( 3^{4} \cdot 7^{2} \)
$0$
$\Z/2\Z\oplus\Z/4\Z$
$\Q$
$\mathrm{SU}(2)$
✓
$2$
8.48.0.24
2Cs
$1$
$1$
$6$
$1$
$-0.618942$
$7189057/3969$
$[1, 0, 0, -4, -1]$
\(y^2+xy=x^3-4x-1\)
21.a6
21a4
21.a
21a
$6$
$8$
\( 3 \cdot 7 \)
\( - 3^{2} \cdot 7 \)
$0$
$\Z/4\Z$
$\Q$
$\mathrm{SU}(2)$
✓
$2$
16.48.0.27
2B
$1$
$1$
$3$
$2$
$-0.965515$
$103823/63$
$[1, 0, 0, 1, 0]$
\(y^2+xy=x^3+x\)
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