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
10.4-a1
10.4-a
$4$
$14$
\(\Q(\sqrt{-31}) \)
$2$
$[0, 1]$
10.4
\( 2 \cdot 5 \)
\( 2^{26} \cdot 5^{7} \)
$0.88475$
$(2,a+1), (5,a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 7$
2B , 7B.2.3
$1$
\( 2 \cdot 7 \)
$1$
$1.385680830$
1.742129368
\( \frac{780929100411181}{1280000000} a - \frac{336050998176533}{160000000} \)
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 62 a + 289\) , \( -550 a + 1785\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+a{x}^2+\left(62a+289\right){x}-550a+1785$
10.4-a2
10.4-a
$4$
$14$
\(\Q(\sqrt{-31}) \)
$2$
$[0, 1]$
10.4
\( 2 \cdot 5 \)
\( 2^{14} \cdot 5 \)
$0.88475$
$(2,a+1), (5,a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 7$
2B , 7B.2.1
$1$
\( 2 \)
$1$
$9.699765812$
1.742129368
\( -\frac{2911}{20} a - \frac{47529}{5} \)
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -3 a - 6\) , \( -4 a + 7\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+a{x}^2+\left(-3a-6\right){x}-4a+7$
10.4-a3
10.4-a
$4$
$14$
\(\Q(\sqrt{-31}) \)
$2$
$[0, 1]$
10.4
\( 2 \cdot 5 \)
\( 2 \cdot 5^{2} \)
$0.88475$
$(2,a+1), (5,a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 7$
2B , 7B.2.1
$1$
\( 2 \)
$1$
$9.699765812$
1.742129368
\( \frac{19951}{50} a - \frac{33947}{25} \)
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( a - 2\) , \( -1\bigr] \)
${y}^2+{x}{y}={x}^3+\left(a+1\right){x}^2+\left(a-2\right){x}-1$
10.4-a4
10.4-a
$4$
$14$
\(\Q(\sqrt{-31}) \)
$2$
$[0, 1]$
10.4
\( 2 \cdot 5 \)
\( 2^{7} \cdot 5^{14} \)
$0.88475$
$(2,a+1), (5,a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 7$
2B , 7B.2.3
$1$
\( 2 \cdot 7 \)
$1$
$1.385680830$
1.742129368
\( -\frac{379001974281391}{781250000000} a + \frac{34453608603063}{97656250000} \)
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 6 a + 13\) , \( -7 a + 24\bigr] \)
${y}^2+{x}{y}={x}^3+\left(a+1\right){x}^2+\left(6a+13\right){x}-7a+24$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.