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
4800.1-b2 4800.1-b $4$
$4$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
4800.1
\( 2^{6} \cdot 3 \cdot 5^{2} \)
\( 2^{20} \cdot 3^{4} \cdot 5^{4} \)
$1.28828$
$(-2a+1), (2), (5)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2Cs $1$
\( 2^{4} \)
$1$
$1.740793442$
2.010095125
\( \frac{470596}{225} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( -16 a + 16\) , \( -16\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-16a+16\right){x}-16$
19200.1-a2 19200.1-a $4$
$4$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
19200.1
\( 2^{8} \cdot 3 \cdot 5^{2} \)
\( 2^{20} \cdot 3^{4} \cdot 5^{4} \)
$1.82190$
$(-2a+1), (2), (5)$
$2$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2Cs $1$
\( 2^{4} \)
$0.333808752$
$1.740793442$
2.683949384
\( \frac{470596}{225} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -16\) , \( 16\bigr] \) ${y}^2={x}^{3}-{x}^{2}-16{x}+16$
57600.1-c2 57600.1-c $4$
$4$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
57600.1
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \)
\( 2^{20} \cdot 3^{10} \cdot 5^{4} \)
$2.39775$
$(-2a+1), (2), (5)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2Cs $1$
\( 2^{5} \)
$1$
$1.005047562$
2.321057923
\( \frac{470596}{225} \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -48 a\) , \( -96 a + 48\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}-48a{x}-96a+48$
57600.1-r2 57600.1-r $4$
$4$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
57600.1
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \)
\( 2^{20} \cdot 3^{10} \cdot 5^{4} \)
$2.39775$
$(-2a+1), (2), (5)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2Cs $1$
\( 2^{5} \)
$1$
$1.005047562$
2.321057923
\( \frac{470596}{225} \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 50 a - 49\) , \( 47 a + 1\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(50a-49\right){x}+47a+1$
120000.1-a2 120000.1-a $4$
$4$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
120000.1
\( 2^{6} \cdot 3 \cdot 5^{4} \)
\( 2^{20} \cdot 3^{4} \cdot 5^{16} \)
$2.88068$
$(-2a+1), (2), (5)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2Cs $4$
\( 2^{4} \)
$1$
$0.348158688$
1.608076100
\( \frac{470596}{225} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -408\) , \( -1188\bigr] \) ${y}^2={x}^{3}-{x}^{2}-408{x}-1188$
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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.
