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
676.1-a1
676.1-a
$2$
$7$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
676.1
\( 2^{2} \cdot 13^{2} \)
\( 2^{2} \cdot 13^{14} \)
$3.31714$
$(a), (a-1), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$7$
7B.1.3
$1$
\( 1 \)
$54.68138223$
$0.385597965$
5.792503149
\( -\frac{1064019559329}{125497034} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -213\) , \( -1257\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-213{x}-1257$
676.1-a2
676.1-a
$2$
$7$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
676.1
\( 2^{2} \cdot 13^{2} \)
\( 2^{14} \cdot 13^{2} \)
$3.31714$
$(a), (a-1), (2)$
$1$
$\Z/7\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$7$
7B.1.1
$1$
\( 7 \)
$7.811626033$
$18.89430030$
5.792503149
\( -\frac{2146689}{1664} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-3{x}+3$
676.1-b1
676.1-b
$1$
$1$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
676.1
\( 2^{2} \cdot 13^{2} \)
\( 2^{10} \cdot 13^{4} \)
$3.31714$
$(a), (a-1), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$1$
\( 2^{2} \)
$1$
$7.905395568$
4.343558374
\( -\frac{2262381966750933}{5408} \)
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -19146 a - 60171\) , \( 2758003 a + 8660351\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-19146a-60171\right){x}+2758003a+8660351$
676.1-c1
676.1-c
$3$
$9$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
676.1
\( 2^{2} \cdot 13^{2} \)
\( 2^{18} \cdot 13^{2} \)
$3.31714$
$(a), (a-1), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.2
$1$
\( 3^{2} \)
$8.538195671$
$0.265819283$
5.611605813
\( -\frac{10730978619193}{6656} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -460\) , \( -3830\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-460{x}-3830$
676.1-c2
676.1-c
$3$
$9$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
676.1
\( 2^{2} \cdot 13^{2} \)
\( 2^{6} \cdot 13^{6} \)
$3.31714$
$(a), (a-1), (2)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3Cs.1.1
$1$
\( 3^{3} \)
$2.846065223$
$2.392373550$
5.611605813
\( -\frac{10218313}{17576} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -5\) , \( -8\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-5{x}-8$
676.1-c3
676.1-c
$3$
$9$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
676.1
\( 2^{2} \cdot 13^{2} \)
\( 2^{2} \cdot 13^{2} \)
$3.31714$
$(a), (a-1), (2)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.1
$1$
\( 1 \)
$8.538195671$
$21.53136195$
5.611605813
\( \frac{12167}{26} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}$
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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.