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
35.1-a1
35.1-a
$2$
$2$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
35.1
\( 5 \cdot 7 \)
\( - 5^{8} \cdot 7^{2} \)
$1.17045$
$(-a-1), (a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$9.170464641$
1.702912532
\( -\frac{34387992882}{19140625} a + \frac{16001575137}{2734375} \)
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 2 a + 3\) , \( -15 a - 34\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a+3\right){x}-15a-34$
175.5-d1
175.5-d
$2$
$2$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
175.5
\( 5^{2} \cdot 7 \)
\( - 5^{14} \cdot 7^{2} \)
$1.75024$
$(-a-1), (a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$0.580216012$
$4.101156464$
1.767490306
\( -\frac{34387992882}{19140625} a + \frac{16001575137}{2734375} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( 8 a - 17\) , \( -22 a + 30\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(8a-17\right){x}-22a+30$
245.3-b1
245.3-b
$2$
$2$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
245.3
\( 5 \cdot 7^{2} \)
\( - 5^{8} \cdot 7^{8} \)
$1.90383$
$(-a-1), (a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{5} \)
$1$
$2.391169248$
3.552231858
\( -\frac{34387992882}{19140625} a + \frac{16001575137}{2734375} \)
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 15 a + 25\) , \( -115 a - 266\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(15a+25\right){x}-115a-266$
875.2-j1
875.2-j
$2$
$2$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
875.2
\( 5^{3} \cdot 7 \)
\( - 5^{14} \cdot 7^{2} \)
$2.61722$
$(-a-1), (-a+2), (a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{6} \)
$0.130114955$
$4.101156464$
3.170914513
\( -\frac{34387992882}{19140625} a + \frac{16001575137}{2734375} \)
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 78 a - 249\) , \( -502 a + 1601\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(78a-249\right){x}-502a+1601$
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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.