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
5625.3-a2 5625.3-a $2$
$5$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
5625.3
\( 3^{2} \cdot 5^{4} \)
\( 3^{10} \cdot 5^{4} \)
$1.54774$
$(-a-2), (2a+1), (3)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$5$
5B.1.1 $1$
\( 5 \)
$1$
$3.274603091$
0.654920618
\( \frac{20480}{243} \)
\( \bigl[0\) , \( -1\) , \( i\) , \( 2\) , \( -4\bigr] \) ${y}^2+i{y}={x}^{3}-{x}^{2}+2{x}-4$
5625.3-c2 5625.3-c $2$
$5$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
5625.3
\( 3^{2} \cdot 5^{4} \)
\( 3^{10} \cdot 5^{16} \)
$1.54774$
$(-a-2), (2a+1), (3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$5$
5B.1.4 $1$
\( 5 \)
$1$
$0.654920618$
3.274603091
\( \frac{20480}{243} \)
\( \bigl[0\) , \( 1\) , \( i\) , \( 42\) , \( -443\bigr] \) ${y}^2+i{y}={x}^{3}+{x}^{2}+42{x}-443$
50625.3-a2 50625.3-a $2$
$5$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
50625.3
\( 3^{4} \cdot 5^{4} \)
\( 3^{22} \cdot 5^{16} \)
$2.68077$
$(-a-2), (2a+1), (3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$5$
5B.4.1 $1$
\( 2^{2} \cdot 3^{2} \)
$0.127940452$
$0.218306872$
2.010980162
\( \frac{20480}{243} \)
\( \bigl[0\) , \( 0\) , \( i\) , \( 375\) , \( 12344\bigr] \) ${y}^2+i{y}={x}^{3}+375{x}+12344$
50625.3-g2 50625.3-g $2$
$5$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
50625.3
\( 3^{4} \cdot 5^{4} \)
\( 3^{22} \cdot 5^{4} \)
$2.68077$
$(-a-2), (2a+1), (3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$5$
5B.4.1 $1$
\( 2^{2} \)
$0.918330811$
$1.091534363$
8.019117100
\( \frac{20480}{243} \)
\( \bigl[0\) , \( 0\) , \( i\) , \( 15\) , \( 99\bigr] \) ${y}^2+i{y}={x}^{3}+15{x}+99$
90000.3-g2 90000.3-g $2$
$5$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
90000.3
\( 2^{4} \cdot 3^{2} \cdot 5^{4} \)
\( 2^{12} \cdot 3^{10} \cdot 5^{10} \)
$3.09549$
$(a+1), (-a-2), (2a+1), (3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$5$
5B.4.1 $1$
\( 3 \)
$1$
$0.732223511$
2.196670533
\( \frac{20480}{243} \)
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -26 i + 20\) , \( -324 i + 74\bigr] \) ${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(-26i+20\right){x}-324i+74$
90000.3-j2 90000.3-j $2$
$5$
\(\Q(\sqrt{-1}) \) $2$
$[0, 1]$
90000.3
\( 2^{4} \cdot 3^{2} \cdot 5^{4} \)
\( 2^{12} \cdot 3^{10} \cdot 5^{10} \)
$3.09549$
$(a+1), (-a-2), (2a+1), (3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$5$
5B.4.1 $1$
\( 3 \)
$1$
$0.732223511$
2.196670533
\( \frac{20480}{243} \)
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 26 i + 20\) , \( 324 i + 74\bigr] \) ${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(26i+20\right){x}+324i+74$
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Pari/GP
SageMath
Magma
Oscar
CSV
*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.
