Label
Class
Class size
Class degree
Base field
Field degree
Field signature
Conductor
Conductor norm
Discriminant norm
Root analytic conductor
Bad primes
Rank
Torsion
CM
CM
Sato-Tate
$\Q$-curve
Base change
Semistable
Potentially good
Nonmax $\ell$
mod-$\ell$ images
$Ш_{\textrm{an}}$
Tamagawa
Regulator
Period
Leading coeff
j-invariant
Weierstrass coefficients
Weierstrass equation
256.1-a1
256.1-a
$2$
$2$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
256.1
\( 2^{8} \)
\( 2^{20} \)
$1.63798$
$(2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$12.75994948$
2.784449256
\( -10220 a - 17724 \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -3 a - 4\) , \( 5 a + 8\bigr] \)
${y}^2={x}^{3}-{x}^{2}+\left(-3a-4\right){x}+5a+8$
256.1-f1
256.1-f
$2$
$2$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
256.1
\( 2^{8} \)
\( 2^{20} \)
$1.63798$
$(2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$0.787454598$
$4.856120083$
1.668919117
\( -10220 a - 17724 \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -3 a - 4\) , \( -5 a - 8\bigr] \)
${y}^2={x}^{3}+{x}^{2}+\left(-3a-4\right){x}-5a-8$
256.1-h1
256.1-h
$2$
$2$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
256.1
\( 2^{8} \)
\( 2^{20} \)
$1.63798$
$(2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$4.856120083$
1.059692279
\( -10220 a - 17724 \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( -5 a + 16\) , \( -17 a + 47\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(-5a+16\right){x}-17a+47$
256.1-i1
256.1-i
$2$
$2$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
256.1
\( 2^{8} \)
\( 2^{20} \)
$1.63798$
$(2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$0.561416932$
$12.75994948$
3.126473920
\( -10220 a - 17724 \)
\( \bigl[0\) , \( a\) , \( 0\) , \( -5 a + 16\) , \( 17 a - 47\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+\left(-5a+16\right){x}+17a-47$
1600.2-a1
1600.2-a
$2$
$2$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1600.2
\( 2^{6} \cdot 5^{2} \)
\( 2^{20} \cdot 5^{6} \)
$2.58987$
$(-a), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$9$
\( 2^{2} \)
$1$
$1.666457050$
3.272856675
\( -10220 a - 17724 \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -18 a + 47\) , \( 63 a - 177\bigr] \)
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-18a+47\right){x}+63a-177$
1600.2-g1
1600.2-g
$2$
$2$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1600.2
\( 2^{6} \cdot 5^{2} \)
\( 2^{20} \cdot 5^{6} \)
$2.58987$
$(-a), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$7.436596934$
1.622798493
\( -10220 a - 17724 \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( -22 a - 35\) , \( 103 a + 190\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(-22a-35\right){x}+103a+190$
1600.3-d1
1600.3-d
$2$
$2$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1600.3
\( 2^{6} \cdot 5^{2} \)
\( 2^{20} \cdot 5^{6} \)
$2.58987$
$(-a+1), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$7.436596934$
1.622798493
\( -10220 a - 17724 \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -11 a - 9\) , \( 23 a + 62\bigr] \)
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-11a-9\right){x}+23a+62$
1600.3-i1
1600.3-i
$2$
$2$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
1600.3
\( 2^{6} \cdot 5^{2} \)
\( 2^{20} \cdot 5^{6} \)
$2.58987$
$(-a+1), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$1.666457050$
0.363650741
\( -10220 a - 17724 \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -41 a + 113\) , \( 285 a - 797\bigr] \)
${y}^2={x}^{3}+{x}^{2}+\left(-41a+113\right){x}+285a-797$
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*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.