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
45625.1-a1
45625.1-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
45625.1
\( 5^{4} \cdot 73 \)
\( 5^{12} \cdot 73^{3} \)
$2.26204$
$(-9a+1), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B[2]
$1$
\( 2 \)
$6.218135797$
$0.648466817$
4.656046711
\( \frac{60988685561}{389017} a - \frac{169775626841}{389017} \)
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 245 a - 366\) , \( -2388 a + 2264\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(245a-366\right){x}-2388a+2264$
45625.1-a2
45625.1-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
45625.1
\( 5^{4} \cdot 73 \)
\( 5^{12} \cdot 73^{2} \)
$2.26204$
$(-9a+1), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B[2]
$1$
\( 2^{3} \)
$1.036355966$
$0.972700226$
4.656046711
\( -\frac{927841113}{5329} a - \frac{395933743}{5329} \)
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -5 a + 134\) , \( -638 a + 264\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-5a+134\right){x}-638a+264$
45625.1-a3
45625.1-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
45625.1
\( 5^{4} \cdot 73 \)
\( 5^{12} \cdot 73 \)
$2.26204$
$(-9a+1), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B[2]
$1$
\( 2 \)
$2.072711932$
$1.945400453$
4.656046711
\( \frac{9927}{73} a + \frac{20960}{73} \)
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -5 a + 9\) , \( -13 a + 14\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-5a+9\right){x}-13a+14$
45625.1-a4
45625.1-a
$4$
$6$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
45625.1
\( 5^{4} \cdot 73 \)
\( 5^{12} \cdot 73^{6} \)
$2.26204$
$(-9a+1), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B[2]
$1$
\( 2^{3} \)
$3.109067898$
$0.324233408$
4.656046711
\( -\frac{55816089234767}{151334226289} a + \frac{107352826006104}{151334226289} \)
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 120 a - 366\) , \( -3763 a + 1639\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(120a-366\right){x}-3763a+1639$
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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.