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
5202.5-g2
5202.5-g
$2$
$2$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
5202.5
\( 2 \cdot 3^{2} \cdot 17^{2} \)
\( 2^{10} \cdot 3^{12} \cdot 17^{3} \)
$2.14648$
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \cdot 5 \)
$1$
$1.090795502$
3.856544483
\( \frac{2091127194353}{409563864} a + \frac{36587816460805}{1638255456} \)
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 29 a - 57\) , \( 100 a - 131\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(29a-57\right){x}+100a-131$
41616.5-m2
41616.5-m
$2$
$2$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
41616.5
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \)
\( 2^{22} \cdot 3^{12} \cdot 17^{3} \)
$3.60993$
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \cdot 11 \)
$0.244349942$
$0.545397751$
4.146324253
\( \frac{2091127194353}{409563864} a + \frac{36587816460805}{1638255456} \)
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 121 a - 224\) , \( 1028 a - 811\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(121a-224\right){x}+1028a-811$
46818.8-b2
46818.8-b
$2$
$2$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
46818.8
\( 2 \cdot 3^{4} \cdot 17^{2} \)
\( 2^{10} \cdot 3^{24} \cdot 17^{3} \)
$3.71781$
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{4} \)
$1$
$0.363598500$
1.028411862
\( \frac{2091127194353}{409563864} a + \frac{36587816460805}{1638255456} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( 270 a - 504\) , \( -3488 a + 3512\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(270a-504\right){x}-3488a+3512$
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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.