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
10.1-a1
10.1-a
$6$
$8$
3.3.733.1
$3$
$[3, 0]$
10.1
\( 2 \cdot 5 \)
\( 2^{4} \cdot 5^{2} \)
$3.55105$
$(a^2-6), (-a+3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$126.0013261$
2.326982585
\( \frac{42724081}{400} a^{2} - \frac{180314633}{400} a + \frac{203829169}{400} \)
\( \bigl[a^{2} - 5\) , \( -a^{2} - a + 4\) , \( a\) , \( -254283425430303815 a^{2} - 386052765748533969 a + 807826405432831715\) , \( -128265428101555296555965052 a^{2} - 194732406112317607687625258 a + 407483104922159986550542545\bigr] \)
${y}^2+\left(a^{2}-5\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-254283425430303815a^{2}-386052765748533969a+807826405432831715\right){x}-128265428101555296555965052a^{2}-194732406112317607687625258a+407483104922159986550542545$
50.2-c5
50.2-c
$6$
$8$
3.3.733.1
$3$
$[3, 0]$
50.2
\( 2 \cdot 5^{2} \)
\( 2^{4} \cdot 5^{8} \)
$4.64357$
$(a^2-6), (-a+3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{4} \)
$1$
$44.91956525$
1.659141999
\( \frac{42724081}{400} a^{2} - \frac{180314633}{400} a + \frac{203829169}{400} \)
\( \bigl[a + 1\) , \( -a^{2} - a + 6\) , \( a^{2} + a - 4\) , \( -78197826161174 a^{2} - 118719837968040 a + 248424641572868\) , \( -691710806524498198688 a^{2} - 1050154446775467734780 a + 2197478083709730946512\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(-78197826161174a^{2}-118719837968040a+248424641572868\right){x}-691710806524498198688a^{2}-1050154446775467734780a+2197478083709730946512$
80.3-a5
80.3-a
$6$
$8$
3.3.733.1
$3$
$[3, 0]$
80.3
\( 2^{4} \cdot 5 \)
\( 2^{16} \cdot 5^{2} \)
$5.02195$
$(a^2-6), (-a+3)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$2.653147090$
$26.86943903$
3.949655339
\( \frac{42724081}{400} a^{2} - \frac{180314633}{400} a + \frac{203829169}{400} \)
\( \bigl[a\) , \( a^{2} - 4\) , \( a^{2} + a - 4\) , \( -24503 a^{2} - 37200 a + 77845\) , \( -3868666 a^{2} - 5873399 a + 12290258\bigr] \)
${y}^2+a{x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-24503a^{2}-37200a+77845\right){x}-3868666a^{2}-5873399a+12290258$
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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.