The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 2059 over totally real cubic fields with discriminant 1957
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
25.3-a1 25.3-a $4$
$4$
3.3.169.1 $3$
$[3, 0]$
25.3
\( 5^{2} \)
\( 5^{5} \)
$1.98642$
$(-a^2+2a+3), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2 \)
$1$
$26.12884281$
1.004955493
\( \frac{53152820281148}{625} a^{2} + \frac{88975367883001}{625} a + \frac{21722839234996}{625} \)
\( \bigl[a\) , \( a^{2} - a - 4\) , \( a\) , \( -52 a^{2} - 78 a - 20\) , \( -511 a^{2} - 821 a - 173\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-52a^{2}-78a-20\right){x}-511a^{2}-821a-173$
25.3-a2 25.3-a $4$
$4$
3.3.169.1 $3$
$[3, 0]$
25.3
\( 5^{2} \)
\( 5^{4} \)
$1.98642$
$(-a^2+2a+3), (-a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2Cs $1$
\( 2^{2} \)
$1$
$52.25768563$
1.004955493
\( \frac{217317341}{5} a^{2} - \frac{2574843704}{25} a - \frac{785560232}{25} \)
\( \bigl[a\) , \( a^{2} - a - 4\) , \( a\) , \( -7 a^{2} + 2 a + 5\) , \( -12 a^{2} - 10 a - 3\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-7a^{2}+2a+5\right){x}-12a^{2}-10a-3$
25.3-a3 25.3-a $4$
$4$
3.3.169.1 $3$
$[3, 0]$
25.3
\( 5^{2} \)
\( 5^{2} \)
$1.98642$
$(-a^2+2a+3), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 1 \)
$1$
$52.25768563$
1.004955493
\( -\frac{18759}{5} a^{2} + \frac{39689}{5} a + \frac{24453}{5} \)
\( \bigl[a\) , \( a^{2} - a - 4\) , \( a\) , \( -2 a^{2} + 2 a + 5\) , \( -a - 2\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-2a^{2}+2a+5\right){x}-a-2$
25.3-a4 25.3-a $4$
$4$
3.3.169.1 $3$
$[3, 0]$
25.3
\( 5^{2} \)
\( - 5^{5} \)
$1.98642$
$(-a^2+2a+3), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2^{2} \)
$1$
$13.06442140$
1.004955493
\( \frac{5230339383024320708}{625} a^{2} - \frac{2486715541714430821}{125} a - \frac{3797798826756471012}{625} \)
\( \bigl[a\) , \( a^{2} - a - 4\) , \( a\) , \( -42 a^{2} + 82 a + 30\) , \( -181 a^{2} + 405 a + 123\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-42a^{2}+82a+30\right){x}-181a^{2}+405a+123$
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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.
