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
84.1-a3 84.1-a $4$
$6$
\(\Q(\sqrt{-42}) \) $2$
$[0, 1]$
84.1
\( 2^{2} \cdot 3 \cdot 7 \)
\( 2^{4} \cdot 3^{12} \cdot 7^{14} \)
$3.50641$
$(2,a), (3,a), (7,a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2, 3$
2B , 3B.1.2 $4$
\( 2^{2} \)
$1.490584847$
$2.617295530$
4.815870580
\( \frac{9826000}{5103} \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( -303\) , \( 477\bigr] \) ${y}^2+a{x}{y}={x}^3-{x}^2-303{x}+477$
84.1-c3 84.1-c $4$
$6$
\(\Q(\sqrt{-210}) \) $2$
$[0, 1]$
84.1
\( 2^{2} \cdot 3 \cdot 7 \)
\( 2^{4} \cdot 3^{12} \cdot 7^{14} \)
$7.84058$
$(2,a), (3,a), (7,a)$
$2$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2, 3$
2B , 3B $4$
\( 2^{2} \cdot 3 \)
$1.645202563$
$5.234591060$
14.26276514
\( \frac{9826000}{5103} \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( 607\) , \( -279\bigr] \) ${y}^2+a{x}{y}={x}^3-{x}^2+607{x}-279$
252.1-b3 252.1-b $4$
$6$
\(\Q(\sqrt{14}) \) $2$
$[2, 0]$
252.1
\( 2^{2} \cdot 3^{2} \cdot 7 \)
\( 2^{4} \cdot 3^{12} \cdot 7^{2} \)
$2.66430$
$(-a+4), (-2a+7), (3)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2, 3$
2B , 3B.1.1 $1$
\( 2^{2} \cdot 3^{2} \)
$1.490584847$
$9.594978077$
3.822404740
\( \frac{9826000}{5103} \)
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -853 a - 3169\) , \( -8575 a - 32064\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-853a-3169\right){x}-8575a-32064$
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Pari/GP
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Magma
Oscar
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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.
