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
98.1-d1
98.1-d
$6$
$18$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
98.1
\( 2 \cdot 7^{2} \)
\( 2^{36} \cdot 7^{2} \)
$1.37737$
$(-a+2), (7)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{2} \cdot 3^{2} \)
$1$
$7.027708105$
1.434524910
\( -\frac{548347731625}{1835008} \)
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 3411 a - 8354\) , \( -169592 a + 415414\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(3411a-8354\right){x}-169592a+415414$
98.1-g1
98.1-g
$6$
$18$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
98.1
\( 2 \cdot 7^{2} \)
\( 2^{36} \cdot 7^{2} \)
$1.37737$
$(-a+2), (7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2 \)
$13.29619660$
$0.436190660$
1.183854065
\( -\frac{548347731625}{1835008} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-171{x}-874$
784.1-f1
784.1-f
$6$
$18$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
784.1
\( 2^{4} \cdot 7^{2} \)
\( 2^{48} \cdot 7^{2} \)
$2.31645$
$(-a+2), (7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$9$
\( 2^{2} \)
$6.314005577$
$0.218095330$
5.059623633
\( -\frac{548347731625}{1835008} \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( -682\) , \( -6990\bigr] \)
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-682{x}-6990$
784.1-k1
784.1-k
$6$
$18$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
784.1
\( 2^{4} \cdot 7^{2} \)
\( 2^{48} \cdot 7^{2} \)
$2.31645$
$(-a+2), (7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$3.484059793$
$3.513854052$
4.997970562
\( -\frac{548347731625}{1835008} \)
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -13642 a - 33423\) , \( 1370379 a + 3356729\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-13642a-33423\right){x}+1370379a+3356729$
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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.