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
1250.3-a2
1250.3-a
$4$
$15$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
1250.3
\( 2 \cdot 5^{4} \)
\( 2^{10} \cdot 5^{16} \)
$1.06266$
$(a+1), (-a-2), (2a+1)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3, 5$
3B.1.1 , 5B.1.4
$1$
\( 2 \cdot 3^{2} \)
$0.324496049$
$0.854500048$
1.109127558
\( -\frac{121945}{32} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -76\) , \( 298\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-76{x}+298$
1250.3-b2
1250.3-b
$4$
$15$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
1250.3
\( 2 \cdot 5^{4} \)
\( 2^{10} \cdot 5^{4} \)
$1.06266$
$(a+1), (-a-2), (2a+1)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3, 5$
3B , 5B.1.1
$1$
\( 2 \cdot 5 \)
$1$
$4.272500240$
1.709000096
\( -\frac{121945}{32} \)
\( \bigl[i\) , \( -1\) , \( i\) , \( -2\) , \( -1\bigr] \)
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}-2{x}-1$
10000.3-e2
10000.3-e
$4$
$15$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
10000.3
\( 2^{4} \cdot 5^{4} \)
\( 2^{22} \cdot 5^{10} \)
$1.78718$
$(a+1), (-a-2), (2a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3, 5$
3B , 5B.4.1
$1$
\( 2 \)
$1$
$0.955360097$
1.910720194
\( -\frac{121945}{32} \)
\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( -49 i - 36\) , \( 236 i + 43\bigr] \)
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-49i-36\right){x}+236i+43$
10000.3-f2
10000.3-f
$4$
$15$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
10000.3
\( 2^{4} \cdot 5^{4} \)
\( 2^{22} \cdot 5^{10} \)
$1.78718$
$(a+1), (-a-2), (2a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3, 5$
3B , 5B.4.1
$1$
\( 2 \)
$1$
$0.955360097$
1.910720194
\( -\frac{121945}{32} \)
\( \bigl[i + 1\) , \( -i + 1\) , \( i + 1\) , \( 47 i - 36\) , \( 236 i - 43\bigr] \)
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(47i-36\right){x}+236i-43$
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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.