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
49.4-a1 49.4-a $4$
$6$
4.4.2624.1 $4$
$[4, 0]$
49.4
\( 7^{2} \)
\( 7^{6} \)
$7.44552$
$(-a^3+3a^2+a-3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2, 3$
2B , 3B $1$
\( 2 \)
$0.115090895$
$312.5508098$
1.404460983
\( 3292211757861632 a^{3} - 7770967386451264 a^{2} - 7075906078720256 a + 9134646147509504 \)
\( \bigl[a^{3} - a^{2} - 3 a\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a\) , \( 38 a^{3} - 41 a^{2} - 159 a - 66\) , \( -241 a^{3} + 276 a^{2} + 974 a + 319\bigr] \) ${y}^2+\left(a^{3}-a^{2}-3a\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-a^{2}-4a+1\right){x}^{2}+\left(38a^{3}-41a^{2}-159a-66\right){x}-241a^{3}+276a^{2}+974a+319$
49.4-a2 49.4-a $4$
$6$
4.4.2624.1 $4$
$[4, 0]$
49.4
\( 7^{2} \)
\( 7^{6} \)
$7.44552$
$(-a^3+3a^2+a-3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2, 3$
2B , 3B $1$
\( 2 \)
$0.038363631$
$937.6524294$
1.404460983
\( 67584 a^{3} - 160832 a^{2} - 143360 a + 192256 \)
\( \bigl[a^{3} - a^{2} - 3 a\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a\) , \( 3 a^{3} - a^{2} - 9 a - 1\) , \( 3 a^{3} - 7 a - 2\bigr] \) ${y}^2+\left(a^{3}-a^{2}-3a\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-a^{2}-4a+1\right){x}^{2}+\left(3a^{3}-a^{2}-9a-1\right){x}+3a^{3}-7a-2$
49.4-a3 49.4-a $4$
$6$
4.4.2624.1 $4$
$[4, 0]$
49.4
\( 7^{2} \)
\( 7^{6} \)
$7.44552$
$(-a^3+3a^2+a-3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2, 3$
2B , 3B $1$
\( 2^{2} \)
$0.057545447$
$312.5508098$
1.404460983
\( 427641453408640 a^{3} + 331260963910720 a^{2} - 363800343820288 a - 154126073580480 \)
\( \bigl[a^{3} - 2 a^{2} - 2 a + 1\) , \( -a^{3} + 2 a^{2} + 3 a - 2\) , \( a^{2} - 2 a\) , \( 4 a^{3} - 24 a^{2} - 22 a - 8\) , \( 4 a^{3} + 39 a^{2} + 126 a + 47\bigr] \) ${y}^2+\left(a^{3}-2a^{2}-2a+1\right){x}{y}+\left(a^{2}-2a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-2\right){x}^{2}+\left(4a^{3}-24a^{2}-22a-8\right){x}+4a^{3}+39a^{2}+126a+47$
49.4-a4 49.4-a $4$
$6$
4.4.2624.1 $4$
$[4, 0]$
49.4
\( 7^{2} \)
\( 7^{6} \)
$7.44552$
$(-a^3+3a^2+a-3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2, 3$
2B , 3B $1$
\( 2^{2} \)
$0.019181815$
$937.6524294$
1.404460983
\( 8064 a^{3} + 9536 a^{2} - 7936 a - 3776 \)
\( \bigl[a^{3} - 2 a^{2} - 2 a + 1\) , \( -a^{3} + 2 a^{2} + 3 a - 2\) , \( a^{2} - 2 a\) , \( -a^{3} + a^{2} + 3 a + 2\) , \( a^{3} - 2 a^{2} - 2 a - 1\bigr] \) ${y}^2+\left(a^{3}-2a^{2}-2a+1\right){x}{y}+\left(a^{2}-2a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-2\right){x}^{2}+\left(-a^{3}+a^{2}+3a+2\right){x}+a^{3}-2a^{2}-2a-1$
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Pari/GP
SageMath
Magma
Oscar
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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.
