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
34.1-a1 34.1-a $4$
$4$
3.3.316.1 $3$
$[3, 0]$
34.1
\( 2 \cdot 17 \)
\( - 2 \cdot 17 \)
$2.85909$
$(-a+1), (-a^2-a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 1 \)
$1$
$166.7838221$
2.345580754
\( \frac{408395021}{34} a^{2} - \frac{574555591}{17} a + \frac{225234634}{17} \)
\( \bigl[1\) , \( a^{2} - 4\) , \( a^{2} + a - 3\) , \( 31 a^{2} - 17 a - 132\) , \( -112 a^{2} + 58 a + 473\bigr] \) ${y}^2+{x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(31a^{2}-17a-132\right){x}-112a^{2}+58a+473$
34.1-a2 34.1-a $4$
$4$
3.3.316.1 $3$
$[3, 0]$
34.1
\( 2 \cdot 17 \)
\( 2 \cdot 17^{4} \)
$2.85909$
$(-a+1), (-a^2-a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2 \)
$1$
$83.39191108$
2.345580754
\( -\frac{159309448818515151}{167042} a^{2} + \frac{42162566237623294}{83521} a + \frac{338464118880741674}{83521} \)
\( \bigl[1\) , \( 0\) , \( a^{2} - 3\) , \( 68502161 a^{2} - 36259336 a - 291075321\) , \( -451289674314 a^{2} + 238875107051 a + 1917593249559\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(68502161a^{2}-36259336a-291075321\right){x}-451289674314a^{2}+238875107051a+1917593249559$
34.1-a3 34.1-a $4$
$4$
3.3.316.1 $3$
$[3, 0]$
34.1
\( 2 \cdot 17 \)
\( 2^{2} \cdot 17^{2} \)
$2.85909$
$(-a+1), (-a^2-a+3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2Cs $1$
\( 2^{2} \)
$1$
$166.7838221$
2.345580754
\( -\frac{425772267}{1156} a^{2} + \frac{222426849}{578} a + \frac{1110226703}{578} \)
\( \bigl[1\) , \( 0\) , \( a^{2} - 3\) , \( 4281891 a^{2} - 2266481 a - 18194366\) , \( -7049373774 a^{2} + 3731350409 a + 29953779855\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(4281891a^{2}-2266481a-18194366\right){x}-7049373774a^{2}+3731350409a+29953779855$
34.1-a4 34.1-a $4$
$4$
3.3.316.1 $3$
$[3, 0]$
34.1
\( 2 \cdot 17 \)
\( 2^{4} \cdot 17 \)
$2.85909$
$(-a+1), (-a^2-a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2^{2} \)
$1$
$41.69595554$
2.345580754
\( \frac{22362946326401}{272} a^{2} + \frac{15015858355381}{136} a - \frac{9544891459227}{136} \)
\( \bigl[1\) , \( -a^{2} - a + 2\) , \( a^{2} - 3\) , \( 34458467957 a^{2} - 18239438694 a - 146418873583\) , \( -9030431019955685 a^{2} + 4779956864569160 a + 38371570523670525\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(34458467957a^{2}-18239438694a-146418873583\right){x}-9030431019955685a^{2}+4779956864569160a+38371570523670525$
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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.
