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
1083.2-c1
1083.2-c
$2$
$5$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
1083.2
\( 3 \cdot 19^{2} \)
\( 3^{4} \cdot 19^{10} \)
$0.88788$
$(-2a+1), (-5a+3), (-5a+2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.1.2
$1$
\( 2^{2} \)
$1$
$0.271765830$
1.255232601
\( -\frac{9358714467168256}{22284891} \)
\( \bigl[0\) , \( -a\) , \( 1\) , \( -4390 a + 4390\) , \( -113432\bigr] \)
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(-4390a+4390\right){x}-113432$
61731.2-d1
61731.2-d
$2$
$5$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
61731.2
\( 3^{2} \cdot 19^{3} \)
\( 3^{10} \cdot 19^{16} \)
$2.43964$
$(-2a+1), (-5a+3), (-5a+2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.4.2
$1$
\( 2^{2} \cdot 5 \)
$1$
$0.035996263$
0.831298097
\( -\frac{9358714467168256}{22284891} \)
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 276592 a - 65855\) , \( -18648239 a - 36055987\bigr] \)
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(276592a-65855\right){x}-18648239a-36055987$
61731.3-d1
61731.3-d
$2$
$5$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
61731.3
\( 3^{2} \cdot 19^{3} \)
\( 3^{10} \cdot 19^{16} \)
$2.43964$
$(-2a+1), (-5a+3), (-5a+2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.4.2
$1$
\( 2^{2} \cdot 5 \)
$1$
$0.035996263$
0.831298097
\( -\frac{9358714467168256}{22284891} \)
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 65856 a - 276591\) , \( 18858975 a - 54638371\bigr] \)
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(65856a-276591\right){x}+18858975a-54638371$
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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.