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
57.1-d2 57.1-d $6$
$8$
\(\Q(\sqrt{57}) \) $2$
$[2, 0]$
57.1
\( 3 \cdot 19 \)
\( - 3 \cdot 19 \)
$1.85372$
$(4a+13), (10a-43)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2B $1$
\( 1 \)
$1$
$36.19446804$
0.299629650
\( -\frac{276137246}{57} a + \frac{1180481203}{57} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( 11 a + 36\) , \( 88 a + 288\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(11a+36\right){x}+88a+288$
57.1-g2 57.1-g $6$
$8$
\(\Q(\sqrt{57}) \) $2$
$[2, 0]$
57.1
\( 3 \cdot 19 \)
\( - 3 \cdot 19 \)
$1.85372$
$(4a+13), (10a-43)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2B $1$
\( 1 \)
$7.785547844$
$9.423048177$
4.858622600
\( -\frac{276137246}{57} a + \frac{1180481203}{57} \)
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 543 a - 2315\) , \( 13825 a - 59110\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(543a-2315\right){x}+13825a-59110$
171.1-e2 171.1-e $6$
$8$
\(\Q(\sqrt{57}) \) $2$
$[2, 0]$
171.1
\( 3^{2} \cdot 19 \)
\( - 3^{7} \cdot 19 \)
$2.43964$
$(4a+13), (10a-43)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2 \)
$1$
$15.07895257$
0.998628029
\( -\frac{276137246}{57} a + \frac{1180481203}{57} \)
\( \bigl[1\) , \( a\) , \( 0\) , \( 6 a - 18\) , \( -18 a + 81\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(6a-18\right){x}-18a+81$
171.1-h2 171.1-h $6$
$8$
\(\Q(\sqrt{57}) \) $2$
$[2, 0]$
171.1
\( 3^{2} \cdot 19 \)
\( - 3^{7} \cdot 19 \)
$2.43964$
$(4a+13), (10a-43)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2^{2} \)
$1$
$7.539476287$
0.998628029
\( -\frac{276137246}{57} a + \frac{1180481203}{57} \)
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 9960 a + 32625\) , \( 2264742 a + 7416846\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(9960a+32625\right){x}+2264742a+7416846$
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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.
