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
3200.4-c1 3200.4-c $4$
$4$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
3200.4
\( 2^{7} \cdot 5^{2} \)
\( 2^{19} \cdot 5^{2} \)
$1.77818$
$(a), (-a+1), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2 \)
$1.438296699$
$2.550556986$
2.773093359
\( -\frac{251566}{5} a - \frac{857372}{5} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -12 a - 4\) , \( 28 a - 8\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(-12a-4\right){x}+28a-8$
3200.5-c1 3200.5-c $4$
$4$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
3200.5
\( 2^{7} \cdot 5^{2} \)
\( 2^{19} \cdot 5^{2} \)
$1.77818$
$(a), (-a+1), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2^{3} \)
$0.359574174$
$2.550556986$
2.773093359
\( -\frac{251566}{5} a - \frac{857372}{5} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -12 a - 4\) , \( -28 a + 8\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(-12a-4\right){x}-28a+8$
12800.4-b2 12800.4-b $4$
$4$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
12800.4
\( 2^{9} \cdot 5^{2} \)
\( 2^{25} \cdot 5^{2} \)
$2.51472$
$(a), (-a+1), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2^{2} \)
$1$
$1.803516140$
1.363330055
\( -\frac{251566}{5} a - \frac{857372}{5} \)
\( \bigl[0\) , \( a\) , \( 0\) , \( 8 a + 32\) , \( 76 a - 72\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(8a+32\right){x}+76a-72$
12800.7-b2 12800.7-b $4$
$4$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
12800.7
\( 2^{9} \cdot 5^{2} \)
\( 2^{25} \cdot 5^{2} \)
$2.51472$
$(a), (-a+1), (5)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2^{4} \)
$1$
$1.803516140$
1.363330055
\( -\frac{251566}{5} a - \frac{857372}{5} \)
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 28 a - 20\) , \( -64 a - 32\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(28a-20\right){x}-64a-32$
25600.5-i2 25600.5-i $4$
$4$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
25600.5
\( 2^{10} \cdot 5^{2} \)
\( 2^{25} \cdot 5^{2} \)
$2.99053$
$(a), (-a+1), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2^{3} \)
$1$
$1.803516140$
2.726660110
\( -\frac{251566}{5} a - \frac{857372}{5} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( 8 a + 32\) , \( -76 a + 72\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(8a+32\right){x}-76a+72$
25600.7-i2 25600.7-i $4$
$4$
\(\Q(\sqrt{-7}) \) $2$
$[0, 1]$
25600.7
\( 2^{10} \cdot 5^{2} \)
\( 2^{25} \cdot 5^{2} \)
$2.99053$
$(a), (-a+1), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2^{3} \)
$1$
$1.803516140$
2.726660110
\( -\frac{251566}{5} a - \frac{857372}{5} \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 28 a - 20\) , \( 64 a + 32\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(28a-20\right){x}+64a+32$
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.
