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
49.1-a1
49.1-a
$4$
$6$
4.4.1957.1
$4$
$[4, 0]$
49.1
\( 7^{2} \)
\( - 7^{9} \)
$6.42996$
$(a^2-2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$0.029401742$
$432.7430195$
1.150449917
\( -\frac{9690935416}{343} a^{3} - \frac{12215671997}{343} a^{2} + \frac{16657874830}{343} a + \frac{14201869411}{343} \)
\( \bigl[a^{2} - 2\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a\) , \( -30 a^{3} + 55 a^{2} + 22 a - 15\) , \( -267 a^{3} + 469 a^{2} + 242 a - 153\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(-30a^{3}+55a^{2}+22a-15\right){x}-267a^{3}+469a^{2}+242a-153$
49.1-a2
49.1-a
$4$
$6$
4.4.1957.1
$4$
$[4, 0]$
49.1
\( 7^{2} \)
\( - 7^{8} \)
$6.42996$
$(a^2-2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$0.019601161$
$649.1145293$
1.150449917
\( -\frac{170631953648}{49} a^{3} + \frac{301490635046}{49} a^{2} + \frac{150363436017}{49} a - \frac{96330872074}{49} \)
\( \bigl[a^{2} - 2\) , \( -a^{2} + a + 3\) , \( a^{3} - 4 a - 1\) , \( -63 a^{3} + 23 a^{2} + 227 a - 17\) , \( 162 a^{3} - 125 a^{2} - 566 a + 280\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-63a^{3}+23a^{2}+227a-17\right){x}+162a^{3}-125a^{2}-566a+280$
49.1-a3
49.1-a
$4$
$6$
4.4.1957.1
$4$
$[4, 0]$
49.1
\( 7^{2} \)
\( - 7^{7} \)
$6.42996$
$(a^2-2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$0.009800580$
$1298.229058$
1.150449917
\( \frac{124820}{7} a^{3} - \frac{238513}{7} a^{2} - \frac{74080}{7} a + \frac{71744}{7} \)
\( \bigl[a^{3} - 4 a\) , \( a^{3} - 3 a\) , \( a^{2} - a - 1\) , \( a^{3} - a^{2} - 3 a\) , \( a^{3} - a\bigr] \)
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(a^{3}-3a\right){x}^{2}+\left(a^{3}-a^{2}-3a\right){x}+a^{3}-a$
49.1-a4
49.1-a
$4$
$6$
4.4.1957.1
$4$
$[4, 0]$
49.1
\( 7^{2} \)
\( - 7^{12} \)
$6.42996$
$(a^2-2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$0.058803484$
$216.3715097$
1.150449917
\( \frac{443958861593546408990}{117649} a^{3} + \frac{915220682926034165096}{117649} a^{2} + \frac{110890939600298461445}{117649} a - \frac{215357317054416491281}{117649} \)
\( \bigl[a\) , \( -a^{3} + 3 a + 1\) , \( -a^{3} + a^{2} + 4 a\) , \( -a^{3} - 16 a^{2} + 56 a - 44\) , \( -109 a^{3} + 141 a^{2} + 199 a - 57\bigr] \)
${y}^2+a{x}{y}+\left(-a^{3}+a^{2}+4a\right){y}={x}^{3}+\left(-a^{3}+3a+1\right){x}^{2}+\left(-a^{3}-16a^{2}+56a-44\right){x}-109a^{3}+141a^{2}+199a-57$
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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.