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
9.1-a1 9.1-a $2$
$3$
5.5.65657.1 $5$
$[5, 0]$
9.1
\( 3^{2} \)
\( - 3^{12} \)
$28.52353$
$(-a^4+a^3+4a^2-2a-2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $3$
3B.1.2 $9$
\( 2 \)
$1$
$23.24954646$
1.63322671
\( -\frac{346538649913}{729} a^{4} + \frac{304213159354}{243} a^{3} + \frac{131211798509}{729} a^{2} - \frac{95505911702}{81} a - \frac{199860865145}{729} \)
\( \bigl[-a^{4} + 2 a^{3} + 4 a^{2} - 6 a - 2\) , \( -2 a^{4} + 2 a^{3} + 9 a^{2} - 6 a - 6\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 5 a - 3\) , \( -45 a^{4} + 79 a^{3} + 158 a^{2} - 211 a - 53\) , \( -242 a^{4} + 430 a^{3} + 867 a^{2} - 1149 a - 312\bigr] \) ${y}^2+\left(-a^{4}+2a^{3}+4a^{2}-6a-2\right){x}{y}+\left(-a^{4}+2a^{3}+4a^{2}-5a-3\right){y}={x}^{3}+\left(-2a^{4}+2a^{3}+9a^{2}-6a-6\right){x}^{2}+\left(-45a^{4}+79a^{3}+158a^{2}-211a-53\right){x}-242a^{4}+430a^{3}+867a^{2}-1149a-312$
9.1-a2 9.1-a $2$
$3$
5.5.65657.1 $5$
$[5, 0]$
9.1
\( 3^{2} \)
\( - 3^{8} \)
$28.52353$
$(-a^4+a^3+4a^2-2a-2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $3$
3B.1.1 $1$
\( 2 \)
$1$
$1883.213263$
1.63322671
\( \frac{463637}{9} a^{4} - \frac{90008}{3} a^{3} - \frac{1905559}{9} a^{2} - 8065 a + \frac{82504}{9} \)
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 3\) , \( -a^{4} + 5 a^{2} + 2 a - 4\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} - 8 a - 6\) , \( 2 a^{4} - 2 a^{3} - 13 a^{2} + 9 a + 17\) , \( -58 a^{4} + 72 a^{3} + 271 a^{2} - 176 a - 247\bigr] \) ${y}^2+\left(a^{4}-a^{3}-4a^{2}+3a+3\right){x}{y}+\left(-2a^{4}+3a^{3}+9a^{2}-8a-6\right){y}={x}^{3}+\left(-a^{4}+5a^{2}+2a-4\right){x}^{2}+\left(2a^{4}-2a^{3}-13a^{2}+9a+17\right){x}-58a^{4}+72a^{3}+271a^{2}-176a-247$
9.1-b1 9.1-b $2$
$5$
5.5.65657.1 $5$
$[5, 0]$
9.1
\( 3^{2} \)
\( - 3^{16} \)
$28.52353$
$(-a^4+a^3+4a^2-2a-2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $5$
5B.4.1 $1$
\( 2 \)
$1$
$134.1493644$
1.04707574
\( \frac{747179612}{59049} a^{4} - \frac{4155930605}{19683} a^{3} - \frac{9128857582}{59049} a^{2} + \frac{3220249090}{6561} a + \frac{7149149617}{59049} \)
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 3\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 6 a - 2\) , \( a^{3} - 3 a\) , \( -a^{3} - a^{2} + 2 a + 4\) , \( 2 a^{4} - 3 a^{3} - 10 a^{2} + 7 a + 8\bigr] \) ${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+3\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-6a-2\right){x}^{2}+\left(-a^{3}-a^{2}+2a+4\right){x}+2a^{4}-3a^{3}-10a^{2}+7a+8$
9.1-b2 9.1-b $2$
$5$
5.5.65657.1 $5$
$[5, 0]$
9.1
\( 3^{2} \)
\( - 3^{8} \)
$28.52353$
$(-a^4+a^3+4a^2-2a-2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $5$
5B.4.2 $25$
\( 2 \)
$1$
$5.365974579$
1.04707574
\( \frac{2521498274075249905348265612}{9} a^{4} - \frac{1488610650200171884252903124}{3} a^{3} - \frac{9163877093686100970416615593}{9} a^{2} + 1345476142192101801059271874 a + \frac{3269990960361707860438009855}{9} \)
\( \bigl[a^{3} - 4 a - 1\) , \( -3 a^{4} + 4 a^{3} + 13 a^{2} - 11 a - 10\) , \( a^{2} - 2\) , \( 17 a^{4} + 247 a^{3} - 506 a^{2} - 251 a - 16\) , \( 3325 a^{4} - 6557 a^{3} - 5396 a^{2} + 5378 a + 1457\bigr] \) ${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-3a^{4}+4a^{3}+13a^{2}-11a-10\right){x}^{2}+\left(17a^{4}+247a^{3}-506a^{2}-251a-16\right){x}+3325a^{4}-6557a^{3}-5396a^{2}+5378a+1457$
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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
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