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-d5
98.1-d
$6$
$18$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
98.1
\( 2 \cdot 7^{2} \)
\( 2^{2} \cdot 7^{4} \)
$1.37737$
$(-a+2), (7)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2^{2} \)
$1$
$7.027708105$
1.434524910
\( \frac{128787625}{98} \)
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -211 a - 514\) , \( -2636 a - 6456\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-211a-514\right){x}-2636a-6456$
98.1-g5
98.1-g
$6$
$18$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
98.1
\( 2 \cdot 7^{2} \)
\( 2^{2} \cdot 7^{4} \)
$1.37737$
$(-a+2), (7)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{2} \)
$0.738677589$
$35.33144352$
1.183854065
\( \frac{128787625}{98} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-11{x}+12$
784.1-f5
784.1-f
$6$
$18$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
784.1
\( 2^{4} \cdot 7^{2} \)
\( 2^{14} \cdot 7^{4} \)
$2.31645$
$(-a+2), (7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$0.350778087$
$17.66572176$
5.059623633
\( \frac{128787625}{98} \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( -42\) , \( 98\bigr] \)
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-42{x}+98$
784.1-k5
784.1-k
$6$
$18$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
784.1
\( 2^{4} \cdot 7^{2} \)
\( 2^{14} \cdot 7^{4} \)
$2.31645$
$(-a+2), (7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$1.742029896$
$3.513854052$
4.997970562
\( \frac{128787625}{98} \)
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 842 a - 2063\) , \( 20245 a - 49591\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(842a-2063\right){x}+20245a-49591$
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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.