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
2601.5-c2 2601.5-c $2$
$3$
\(\Q(\sqrt{-2}) \) $2$
$[0, 1]$
2601.5
\( 3^{2} \cdot 17^{2} \)
\( 3^{6} \cdot 17^{2} \)
$1.80496$
$(-a-1), (a-1), (-2a+3), (2a+3)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$3$
3B.1.1 $1$
\( 3^{2} \)
$0.450514168$
$5.038253197$
3.209988236
\( \frac{32768}{459} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( 1\) , \( -1\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}+{x}-1$
23409.8-h2 23409.8-h $2$
$3$
\(\Q(\sqrt{-2}) \) $2$
$[0, 1]$
23409.8
\( 3^{4} \cdot 17^{2} \)
\( 3^{18} \cdot 17^{2} \)
$3.12629$
$(-a-1), (a-1), (-2a+3), (2a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3B.1.2 $1$
\( 2^{4} \)
$0.112889738$
$1.679417732$
4.289910009
\( \frac{32768}{459} \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( 6\) , \( 27\bigr] \) ${y}^2+{y}={x}^{3}+6{x}+27$
41616.5-f2 41616.5-f $2$
$3$
\(\Q(\sqrt{-2}) \) $2$
$[0, 1]$
41616.5
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \)
\( 2^{12} \cdot 3^{6} \cdot 17^{2} \)
$3.60993$
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3B $1$
\( 1 \)
$1.180919587$
$2.519126598$
4.207124047
\( \frac{32768}{459} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( 3\) , \( -9\bigr] \) ${y}^2={x}^{3}-{x}^{2}+3{x}-9$
44217.6-c2 44217.6-c $2$
$3$
\(\Q(\sqrt{-2}) \) $2$
$[0, 1]$
44217.6
\( 3^{2} \cdot 17^{3} \)
\( 3^{6} \cdot 17^{8} \)
$3.66506$
$(-a-1), (a-1), (-2a+3), (2a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3B $1$
\( 2 \cdot 3 \)
$0.427073347$
$1.221955888$
4.428169593
\( \frac{32768}{459} \)
\( \bigl[0\) , \( a\) , \( a + 1\) , \( -8 a\) , \( 38 a + 51\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}-8a{x}+38a+51$
44217.7-c2 44217.7-c $2$
$3$
\(\Q(\sqrt{-2}) \) $2$
$[0, 1]$
44217.7
\( 3^{2} \cdot 17^{3} \)
\( 3^{6} \cdot 17^{8} \)
$3.66506$
$(-a-1), (a-1), (-2a+3), (2a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3B $1$
\( 2 \cdot 3 \)
$0.427073347$
$1.221955888$
4.428169593
\( \frac{32768}{459} \)
\( \bigl[0\) , \( -a\) , \( a + 1\) , \( 8 a\) , \( -39 a + 51\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}-a{x}^{2}+8a{x}-39a+51$
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Pari/GP
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Magma
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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.
