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
23.1-a1 23.1-a $4$
$6$
5.5.70601.1 $5$
$[5, 0]$
23.1
\( 23 \)
\( - 23^{2} \)
$32.48754$
$(a^2-a-3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2, 3$
2B , 3B $1$
\( 2 \)
$0.289345509$
$862.9900285$
2.34940077
\( \frac{390105677339719991}{529} a^{4} - \frac{1089663767831678793}{529} a^{3} + \frac{3510982897333356}{529} a^{2} + \frac{773926975640782522}{529} a - \frac{217539643409513153}{529} \)
\( \bigl[1\) , \( -a^{4} + 7 a^{2} - 6\) , \( a\) , \( -90 a^{4} + 56 a^{3} + 477 a^{2} - 15 a - 294\) , \( 410 a^{4} - 270 a^{3} - 2148 a^{2} + 101 a + 1297\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{4}+7a^{2}-6\right){x}^{2}+\left(-90a^{4}+56a^{3}+477a^{2}-15a-294\right){x}+410a^{4}-270a^{3}-2148a^{2}+101a+1297$
23.1-a2 23.1-a $4$
$6$
5.5.70601.1 $5$
$[5, 0]$
23.1
\( 23 \)
\( -23 \)
$32.48754$
$(a^2-a-3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2, 3$
2B , 3B $1$
\( 1 \)
$0.144672754$
$3451.960114$
2.34940077
\( \frac{244420132}{23} a^{4} - \frac{201883474}{23} a^{3} - \frac{136447512}{23} a^{2} + \frac{150154481}{23} a - \frac{30067803}{23} \)
\( \bigl[1\) , \( -a^{4} + 7 a^{2} - 6\) , \( a\) , \( 25 a^{4} - 19 a^{3} - 128 a^{2} + 10 a + 76\) , \( -7 a^{4} + 5 a^{3} + 40 a^{2} - 3 a - 24\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{4}+7a^{2}-6\right){x}^{2}+\left(25a^{4}-19a^{3}-128a^{2}+10a+76\right){x}-7a^{4}+5a^{3}+40a^{2}-3a-24$
23.1-a3 23.1-a $4$
$6$
5.5.70601.1 $5$
$[5, 0]$
23.1
\( 23 \)
\( - 23^{3} \)
$32.48754$
$(a^2-a-3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2, 3$
2B , 3B $1$
\( 1 \)
$0.048224251$
$10355.88034$
2.34940077
\( -\frac{183399301}{12167} a^{4} + \frac{125042119}{12167} a^{3} + \frac{961492697}{12167} a^{2} - \frac{65243956}{12167} a - \frac{570265911}{12167} \)
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a\) , \( a^{4} - a^{3} - 4 a^{2} + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a - 1\) , \( -a^{3} + a^{2} + 3 a - 1\bigr] \) ${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+1\right){x}^{2}+\left(a^{4}-2a^{3}-3a^{2}+3a-1\right){x}-a^{3}+a^{2}+3a-1$
23.1-a4 23.1-a $4$
$6$
5.5.70601.1 $5$
$[5, 0]$
23.1
\( 23 \)
\( - 23^{6} \)
$32.48754$
$(a^2-a-3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2, 3$
2B , 3B $1$
\( 2 \)
$0.096448503$
$2588.970085$
2.34940077
\( \frac{93598253132532104}{148035889} a^{4} - \frac{63446863598677057}{148035889} a^{3} - \frac{488429136542190831}{148035889} a^{2} + \frac{29836445874686692}{148035889} a + \frac{290435397221009784}{148035889} \)
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a\) , \( a^{4} - a^{3} - 4 a^{2} + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a\) , \( 6 a^{4} - 2 a^{3} - 28 a^{2} - 12 a - 1\) , \( -16 a^{4} + a^{3} + 83 a^{2} + 45 a - 16\bigr] \) ${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+1\right){x}^{2}+\left(6a^{4}-2a^{3}-28a^{2}-12a-1\right){x}-16a^{4}+a^{3}+83a^{2}+45a-16$
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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.
