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-b1
3200.4-b
$1$
$1$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
3200.4
\( 2^{7} \cdot 5^{2} \)
\( 2^{16} \cdot 5^{2} \)
$1.77818$
$(a), (-a+1), (5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2^{2} \)
$0.155429511$
$2.835075283$
2.664827128
\( -\frac{2249728}{5} \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 17\) , \( 27 a - 5\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+17\right){x}+27a-5$
3200.5-a1
3200.5-a
$1$
$1$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
3200.5
\( 2^{7} \cdot 5^{2} \)
\( 2^{16} \cdot 5^{2} \)
$1.77818$
$(a), (-a+1), (5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2^{2} \)
$0.155429511$
$2.835075283$
2.664827128
\( -\frac{2249728}{5} \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 17\) , \( -27 a + 5\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+17\right){x}-27a+5$
12800.4-d1
12800.4-d
$1$
$1$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
12800.4
\( 2^{9} \cdot 5^{2} \)
\( 2^{22} \cdot 5^{2} \)
$2.51472$
$(a), (-a+1), (5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$1$
$2.004700957$
3.030822964
\( -\frac{2249728}{5} \)
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 17 a - 35\) , \( 41 a - 63\bigr] \)
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(17a-35\right){x}+41a-63$
12800.7-d1
12800.7-d
$1$
$1$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
12800.7
\( 2^{9} \cdot 5^{2} \)
\( 2^{22} \cdot 5^{2} \)
$2.51472$
$(a), (-a+1), (5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$1$
$2.004700957$
3.030822964
\( -\frac{2249728}{5} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( -17 a - 18\) , \( -41 a - 22\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(-17a-18\right){x}-41a-22$
25600.5-j1
25600.5-j
$1$
$1$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
25600.5
\( 2^{10} \cdot 5^{2} \)
\( 2^{22} \cdot 5^{2} \)
$2.99053$
$(a), (-a+1), (5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$2.004700957$
1.515411482
\( -\frac{2249728}{5} \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 17 a - 35\) , \( -41 a + 63\bigr] \)
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(17a-35\right){x}-41a+63$
25600.7-j1
25600.7-j
$1$
$1$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
25600.7
\( 2^{10} \cdot 5^{2} \)
\( 2^{22} \cdot 5^{2} \)
$2.99053$
$(a), (-a+1), (5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$2.004700957$
1.515411482
\( -\frac{2249728}{5} \)
\( \bigl[0\) , \( a\) , \( 0\) , \( -17 a - 18\) , \( 41 a + 22\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+\left(-17a-18\right){x}+41a+22$
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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.