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 $1$
$1$
4.4.16997.1 $4$
$[4, 0]$
23.1
\( 23 \)
\( - 23^{5} \)
$17.24014$
$(a^2+2a-1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$1$
\( 1 \)
$1$
$400.8912646$
3.074966976
\( -\frac{66886133}{12167} a^{3} - \frac{146500454}{12167} a^{2} + \frac{46547253}{12167} a + \frac{145466034}{12167} \)
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - 2 a^{2} - 4 a + 5\) , \( a^{3} - a^{2} - 4 a + 3\) , \( -4 a^{3} + 10 a^{2} + a - 7\) , \( 2 a^{3} - 3 a^{2} - 7 a + 7\bigr] \) ${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{3}-a^{2}-4a+3\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+5\right){x}^{2}+\left(-4a^{3}+10a^{2}+a-7\right){x}+2a^{3}-3a^{2}-7a+7$
23.1-b1 23.1-b $1$
$1$
4.4.16997.1 $4$
$[4, 0]$
23.1
\( 23 \)
\( -23 \)
$17.24014$
$(a^2+2a-1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$1$
\( 1 \)
$0.413046127$
$302.5170590$
3.833736665
\( -\frac{135438}{23} a^{3} - \frac{62386}{23} a^{2} + \frac{855483}{23} a + \frac{93087}{23} \)
\( \bigl[a\) , \( -a^{3} + 5 a + 1\) , \( a\) , \( a^{3} - 5 a^{2} + a + 10\) , \( 3 a^{3} - 8 a^{2} - 3 a + 11\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{3}+5a+1\right){x}^{2}+\left(a^{3}-5a^{2}+a+10\right){x}+3a^{3}-8a^{2}-3a+11$
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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.
