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-b1 4800.1-b $4$
$4$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
4800.1
\( 2^{6} \cdot 3 \cdot 5^{2} \)
\( 2^{16} \cdot 3^{2} \cdot 5^{2} \)
$1.28828$
$(-2a+1), (2), (5)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2B $1$
\( 2^{3} \)
$1$
$3.481586885$
2.010095125
\( \frac{21296}{15} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( 4 a - 4\) , \( 0\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(4a-4\right){x}$
19200.1-a1 19200.1-a $4$
$4$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
19200.1
\( 2^{8} \cdot 3 \cdot 5^{2} \)
\( 2^{16} \cdot 3^{2} \cdot 5^{2} \)
$1.82190$
$(-2a+1), (2), (5)$
$2$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2B $1$
\( 2^{3} \)
$0.083452188$
$3.481586885$
2.683949384
\( \frac{21296}{15} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( 4\) , \( 0\bigr] \) ${y}^2={x}^{3}-{x}^{2}+4{x}$
57600.1-c1 57600.1-c $4$
$4$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
57600.1
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \)
\( 2^{16} \cdot 3^{8} \cdot 5^{2} \)
$2.39775$
$(-2a+1), (2), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2^{2} \)
$1$
$2.010095125$
2.321057923
\( \frac{21296}{15} \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 12 a\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+12a{x}$
57600.1-r1 57600.1-r $4$
$4$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
57600.1
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \)
\( 2^{16} \cdot 3^{8} \cdot 5^{2} \)
$2.39775$
$(-2a+1), (2), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2^{2} \)
$1$
$2.010095125$
2.321057923
\( \frac{21296}{15} \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -10 a + 11\) , \( 11 a - 11\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-10a+11\right){x}+11a-11$
120000.1-a1 120000.1-a $4$
$4$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
120000.1
\( 2^{6} \cdot 3 \cdot 5^{4} \)
\( 2^{16} \cdot 3^{2} \cdot 5^{14} \)
$2.88068$
$(-2a+1), (2), (5)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2B $1$
\( 2^{5} \)
$1$
$0.696317377$
1.608076100
\( \frac{21296}{15} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( 92\) , \( -188\bigr] \) ${y}^2={x}^{3}-{x}^{2}+92{x}-188$
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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.
