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
10.1-a1
10.1-a
$4$
$14$
\(\Q(\sqrt{-31}) \)
$2$
$[0, 1]$
10.1
\( 2 \cdot 5 \)
\( 2^{26} \cdot 5^{7} \)
$0.88475$
$(2,a), (5,a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 7$
2B , 7B.2.3
$1$
\( 2 \cdot 7 \)
$1$
$1.385680830$
1.742129368
\( -\frac{780929100411181}{1280000000} a - \frac{1907478885001083}{1280000000} \)
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -67 a + 360\) , \( 905 a + 1396\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^3+\left(a-1\right){x}^2+\left(-67a+360\right){x}+905a+1396$
10.1-a2
10.1-a
$4$
$14$
\(\Q(\sqrt{-31}) \)
$2$
$[0, 1]$
10.1
\( 2 \cdot 5 \)
\( 2^{14} \cdot 5 \)
$0.88475$
$(2,a), (5,a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 7$
2B , 7B.2.1
$1$
\( 2 \)
$1$
$9.699765812$
1.742129368
\( \frac{2911}{20} a - \frac{193027}{20} \)
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -2 a\) , \( -a + 4\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^3+\left(a-1\right){x}^2-2a{x}-a+4$
10.1-a3
10.1-a
$4$
$14$
\(\Q(\sqrt{-31}) \)
$2$
$[0, 1]$
10.1
\( 2 \cdot 5 \)
\( 2 \cdot 5^{2} \)
$0.88475$
$(2,a), (5,a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 7$
2B , 7B.2.1
$1$
\( 2 \)
$1$
$9.699765812$
1.742129368
\( -\frac{19951}{50} a - \frac{47943}{50} \)
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( a - 3\) , \( 1\bigr] \)
${y}^2+{x}{y}+{y}={x}^3+\left(-a-1\right){x}^2+\left(a-3\right){x}+1$
10.1-a4
10.1-a
$4$
$14$
\(\Q(\sqrt{-31}) \)
$2$
$[0, 1]$
10.1
\( 2 \cdot 5 \)
\( 2^{7} \cdot 5^{14} \)
$0.88475$
$(2,a), (5,a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 7$
2B , 7B.2.3
$1$
\( 2 \cdot 7 \)
$1$
$1.385680830$
1.742129368
\( \frac{379001974281391}{781250000000} a - \frac{103373105456887}{781250000000} \)
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -4 a + 17\) , \( 12 a - 1\bigr] \)
${y}^2+{x}{y}+{y}={x}^3+\left(-a-1\right){x}^2+\left(-4a+17\right){x}+12a-1$
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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.