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
10.1-a1
10.1-a
$1$
$1$
4.4.16448.1
$4$
$[4, 0]$
10.1
\( 2 \cdot 5 \)
\( - 2^{5} \cdot 5^{4} \)
$15.28252$
$(a), (-2a^3+5a^2+9a-3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \cdot 5 \)
$0.005502615$
$2194.334899$
3.765958694
\( \frac{100210679}{2500} a^{3} - \frac{90943874}{625} a^{2} - \frac{18207153}{625} a + \frac{79650407}{1250} \)
\( \bigl[a^{3} - 3 a^{2} - 3 a + 3\) , \( a^{3} - 3 a^{2} - 4 a + 2\) , \( a^{3} - 3 a^{2} - 3 a + 2\) , \( 66 a^{3} - 99 a^{2} - 441 a - 230\) , \( -516 a^{3} + 750 a^{2} + 3510 a + 1912\bigr] \)
${y}^2+\left(a^{3}-3a^{2}-3a+3\right){x}{y}+\left(a^{3}-3a^{2}-3a+2\right){y}={x}^{3}+\left(a^{3}-3a^{2}-4a+2\right){x}^{2}+\left(66a^{3}-99a^{2}-441a-230\right){x}-516a^{3}+750a^{2}+3510a+1912$
10.1-b1
10.1-b
$1$
$1$
4.4.16448.1
$4$
$[4, 0]$
10.1
\( 2 \cdot 5 \)
\( - 2^{5} \cdot 5^{4} \)
$15.28252$
$(a), (-2a^3+5a^2+9a-3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2^{2} \)
$0.021941483$
$724.7407107$
1.983864792
\( \frac{100210679}{2500} a^{3} - \frac{90943874}{625} a^{2} - \frac{18207153}{625} a + \frac{79650407}{1250} \)
\( \bigl[a^{3} - 2 a^{2} - 4 a - 1\) , \( -2 a^{3} + 5 a^{2} + 7 a - 1\) , \( 2 a^{3} - 5 a^{2} - 8 a + 2\) , \( -a^{3} + 4 a^{2} - 3 a - 3\) , \( 3 a^{3} - 32 a - 27\bigr] \)
${y}^2+\left(a^{3}-2a^{2}-4a-1\right){x}{y}+\left(2a^{3}-5a^{2}-8a+2\right){y}={x}^{3}+\left(-2a^{3}+5a^{2}+7a-1\right){x}^{2}+\left(-a^{3}+4a^{2}-3a-3\right){x}+3a^{3}-32a-27$
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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.