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
16.1-a1
16.1-a
$2$
$7$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
16.1
\( 2^{4} \)
\( 2^{16} \)
$0.96243$
$(2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$7$
7B
$1$
\( 1 \)
$1$
$6.065863468$
1.126402568
\( -58240 a - 127696 \)
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -2 a - 1\) , \( -3 a - 7\bigr] \)
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a-1\right){x}-3a-7$
256.1-b1
256.1-b
$2$
$7$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
256.1
\( 2^{8} \)
\( 2^{16} \)
$1.92485$
$(2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$7$
7B
$1$
\( 2 \)
$1.290254109$
$3.491576629$
3.346245661
\( -58240 a - 127696 \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( 0\) , \( 20 a - 64\bigr] \)
${y}^2={x}^{3}+{x}^{2}+20a-64$
256.1-k1
256.1-k
$2$
$7$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
256.1
\( 2^{8} \)
\( 2^{16} \)
$1.92485$
$(2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$7$
7B
$1$
\( 2 \)
$0.184322015$
$24.44103640$
3.346245661
\( -58240 a - 127696 \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( 0\) , \( -20 a + 64\bigr] \)
${y}^2={x}^{3}-{x}^{2}-20a+64$
256.1-o1
256.1-o
$2$
$7$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
256.1
\( 2^{8} \)
\( 2^{16} \)
$1.92485$
$(2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$7$
7B
$1$
\( 1 \)
$1$
$14.06852494$
2.612459497
\( -58240 a - 127696 \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -2 a - 1\) , \( 3 a + 7\bigr] \)
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a-1\right){x}+3a+7$
400.2-a1
400.2-a
$2$
$7$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
400.2
\( 2^{4} \cdot 5^{2} \)
\( 2^{16} \cdot 5^{6} \)
$2.15205$
$(-a-1), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$7$
7B
$1$
\( 3 \)
$1$
$2.712736611$
1.511227627
\( -58240 a - 127696 \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 0\) , \( -36 a + 104\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-36a+104$
400.3-a1
400.3-a
$2$
$7$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
400.3
\( 2^{4} \cdot 5^{2} \)
\( 2^{16} \cdot 5^{6} \)
$2.15205$
$(-a+2), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$7$
7B
$1$
\( 3 \)
$1$
$2.712736611$
1.511227627
\( -58240 a - 127696 \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a - 1\) , \( -1475 a + 4711\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(2a-1\right){x}-1475a+4711$
784.2-a1
784.2-a
$2$
$7$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
784.2
\( 2^{4} \cdot 7^{2} \)
\( 2^{16} \cdot 7^{6} \)
$2.54634$
$(-a), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$7$
7B.2.1
$1$
\( 2 \)
$0.628191423$
$9.237843445$
4.310459739
\( -58240 a - 127696 \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -17 a - 37\) , \( 67 a + 155\bigr] \)
${y}^2={x}^{3}-{x}^{2}+\left(-17a-37\right){x}+67a+155$
784.3-a1
784.3-a
$2$
$7$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
784.3
\( 2^{4} \cdot 7^{2} \)
\( 2^{16} \cdot 7^{6} \)
$2.54634$
$(a-1), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$7$
7B.2.3
$1$
\( 2 \)
$4.397339964$
$1.319691920$
4.310459739
\( -58240 a - 127696 \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -7 a - 15\) , \( -5 a - 36\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-7a-15\right){x}-5a-36$
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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.