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
65.3-a1
65.3-a
$6$
$18$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
65.3
\( 5 \cdot 13 \)
\( 5^{9} \cdot 13^{2} \)
$0.50745$
$(2a+1), (-3a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2 \)
$1$
$0.850436644$
0.425218322
\( \frac{157034896049234432}{330078125} a - \frac{128574568523373376}{330078125} \)
\( \bigl[i + 1\) , \( -i\) , \( i\) , \( -240 i - 399\) , \( 2869 i + 2627\bigr] \)
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}-i{x}^{2}+\left(-240i-399\right){x}+2869i+2627$
65.3-a2
65.3-a
$6$
$18$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
65.3
\( 5 \cdot 13 \)
\( 5^{6} \cdot 13^{3} \)
$0.50745$
$(2a+1), (-3a-2)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3Cs.1.1
$1$
\( 2 \cdot 3 \)
$1$
$2.551309934$
0.425218322
\( \frac{2088753403392}{34328125} a - \frac{1627055822656}{34328125} \)
\( \bigl[i + 1\) , \( i - 1\) , \( i\) , \( 14 i + 4\) , \( 7 i + 14\bigr] \)
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(14i+4\right){x}+7i+14$
65.3-a3
65.3-a
$6$
$18$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
65.3
\( 5 \cdot 13 \)
\( 5^{2} \cdot 13 \)
$0.50745$
$(2a+1), (-3a-2)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2 \)
$1$
$7.653929802$
0.425218322
\( -\frac{732672}{325} a - \frac{3306304}{325} \)
\( \bigl[i + 1\) , \( i - 1\) , \( i\) , \( -i - 1\) , \( -i + 1\bigr] \)
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-i-1\right){x}-i+1$
65.3-a4
65.3-a
$6$
$18$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
65.3
\( 5 \cdot 13 \)
\( 5^{18} \cdot 13 \)
$0.50745$
$(2a+1), (-3a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2 \)
$1$
$0.850436644$
0.425218322
\( -\frac{1110974116587520512}{49591064453125} a - \frac{489671365797093184}{49591064453125} \)
\( \bigl[i + 1\) , \( i - 1\) , \( i\) , \( 59 i + 99\) , \( 372 i - 410\bigr] \)
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(59i+99\right){x}+372i-410$
65.3-a5
65.3-a
$6$
$18$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
65.3
\( 5 \cdot 13 \)
\( 5 \cdot 13^{2} \)
$0.50745$
$(2a+1), (-3a-2)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2 \)
$1$
$7.653929802$
0.425218322
\( \frac{1183232}{845} a - \frac{851776}{845} \)
\( \bigl[i + 1\) , \( -i\) , \( i\) , \( 1\) , \( 0\bigr] \)
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}-i{x}^{2}+{x}$
65.3-a6
65.3-a
$6$
$18$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
65.3
\( 5 \cdot 13 \)
\( 5^{3} \cdot 13^{6} \)
$0.50745$
$(2a+1), (-3a-2)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3Cs.1.1
$1$
\( 2 \cdot 3 \)
$1$
$2.551309934$
0.425218322
\( -\frac{356394317312}{603351125} a + \frac{580261889216}{603351125} \)
\( \bigl[i + 1\) , \( -i\) , \( i\) , \( -5 i - 4\) , \( 2 i + 5\bigr] \)
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}-i{x}^{2}+\left(-5i-4\right){x}+2i+5$
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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.