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
2916.1-a2 2916.1-a $2$
$3$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
2916.1
\( 2^{2} \cdot 3^{6} \)
\( 2^{12} \cdot 3^{8} \)
$1.13736$
$(-2a+1), (2)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3B.1.1[2] $1$
\( 2 \cdot 3^{2} \)
$0.101978294$
$3.305583379$
1.556987840
\( \frac{109503}{64} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( 4\) , \( -1\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+4{x}-1$
13122.1-d2 13122.1-d $2$
$3$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
13122.1
\( 2 \cdot 3^{8} \)
\( 2^{12} \cdot 3^{8} \)
$1.91280$
$(a+1), (3)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2, 3$
2Cn , 3B.1.1 $1$
\( 2^{2} \cdot 3 \)
$1$
$3.305583379$
4.407444505
\( \frac{109503}{64} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( 4\) , \( -1\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+4{x}-1$
26244.2-k2 26244.2-k $2$
$3$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
26244.2
\( 2^{2} \cdot 3^{8} \)
\( 2^{12} \cdot 3^{8} \)
$3.00916$
$(a), (-a+1), (3)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3B.1.1 $1$
\( 2^{2} \cdot 3^{2} \)
$0.457897845$
$3.305583379$
9.153510392
\( \frac{109503}{64} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( 4\) , \( -1\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+4{x}-1$
13122.5-g2 13122.5-g $2$
$3$
\(\Q(\sqrt{-2}) \) $2$
$[0, 1]$
13122.5
\( 2 \cdot 3^{8} \)
\( 2^{12} \cdot 3^{8} \)
$2.70510$
$(a), (-a-1), (a-1)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3B.1.1 $1$
\( 2^{2} \cdot 3 \)
$1$
$3.305583379$
3.116533897
\( \frac{109503}{64} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( 4\) , \( -1\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+4{x}-1$
26244.5-d2 26244.5-d $2$
$3$
\(\Q(\sqrt{-11}) \) $2$
$[0, 1]$
26244.5
\( 2^{2} \cdot 3^{8} \)
\( 2^{12} \cdot 3^{8} \)
$3.77218$
$(-a), (a-1), (2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3B.1.1 $4$
\( 2 \cdot 3 \)
$1$
$3.305583379$
5.315578076
\( \frac{109503}{64} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( 4\) , \( -1\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+4{x}-1$
1458.1-k2 1458.1-k $2$
$3$
\(\Q(\sqrt{3}) \) $2$
$[2, 0]$
1458.1
\( 2 \cdot 3^{6} \)
\( 2^{12} \cdot 3^{8} \)
$1.91280$
$(a+1), (a)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3B.1.1 $1$
\( 2^{2} \cdot 3 \)
$1$
$6.786912033$
2.612283659
\( \frac{109503}{64} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( 4\) , \( -1\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+4{x}-1$
648.1-c2 648.1-c $2$
$3$
\(\Q(\zeta_{9})^+\) $3$
$[3, 0]$
648.1
\( 2^{3} \cdot 3^{4} \)
\( - 2^{18} \cdot 3^{12} \)
$2.36579$
$(-a^2+1), (2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3B.1.1 $1$
\( 2 \cdot 3 \)
$1$
$17.68106132$
1.309708246
\( \frac{109503}{64} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( 4\) , \( -1\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+4{x}-1$
2.1-b1 2.1-b $2$
$3$
3.3.1620.1 $3$
$[3, 0]$
2.1
\( 2 \)
\( - 2^{18} \)
$4.03708$
$(a+2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$3$
3B.1.1 $1$
\( 2 \cdot 3^{2} \)
$1$
$53.04318396$
2.635737002
\( \frac{109503}{64} \)
\( \bigl[a^{2} - a - 7\) , \( -a^{2} + 3 a + 9\) , \( a^{2} - 2 a - 7\) , \( -30 a^{2} + 47 a + 317\) , \( -79 a^{2} + 118 a + 807\bigr] \) ${y}^2+\left(a^{2}-a-7\right){x}{y}+\left(a^{2}-2a-7\right){y}={x}^{3}+\left(-a^{2}+3a+9\right){x}^{2}+\left(-30a^{2}+47a+317\right){x}-79a^{2}+118a+807$
Download
displayed columns for
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.
