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
7.2-a4
7.2-a
$4$
$10$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
7.2
\( 7 \)
\( -7 \)
$0.78273$
$(a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B
$1$
\( 1 \)
$1$
$20.28981932$
0.941931215
\( \frac{94831363}{7} a + 24861195 \)
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -5 a - 12\) , \( -6 a - 13\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-5a-12\right){x}-6a-13$
49.3-d4
49.3-d
$4$
$10$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
49.3
\( 7^{2} \)
\( - 7^{7} \)
$1.27317$
$(a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B
$1$
\( 2^{2} \)
$2.994886947$
$1.565140442$
1.740863594
\( \frac{94831363}{7} a + 24861195 \)
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -28 a - 75\) , \( -138 a - 355\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-28a-75\right){x}-138a-355$
175.3-b4
175.3-b
$4$
$10$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
175.3
\( 5^{2} \cdot 7 \)
\( - 5^{6} \cdot 7 \)
$1.75024$
$(-a+2), (a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B
$1$
\( 2^{2} \)
$1$
$9.073883053$
1.684977782
\( \frac{94831363}{7} a + 24861195 \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( 152 a - 487\) , \( -1667 a + 5321\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(152a-487\right){x}-1667a+5321$
175.5-f4
175.5-f
$4$
$10$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
175.5
\( 5^{2} \cdot 7 \)
\( - 5^{6} \cdot 7 \)
$1.75024$
$(-a-1), (a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B
$1$
\( 2 \)
$1.749842318$
$9.073883053$
2.948445428
\( \frac{94831363}{7} a + 24861195 \)
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( 8 a - 50\) , \( -53 a + 105\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(8a-50\right){x}-53a+105$
343.1-c4
343.1-c
$4$
$10$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
343.1
\( 7^{3} \)
\( - 7^{7} \)
$2.07091$
$(-a), (a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B
$1$
\( 2 \)
$1$
$22.01432169$
2.043978456
\( \frac{94831363}{7} a + 24861195 \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -59 a - 135\) , \( 305 a + 685\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-59a-135\right){x}+305a+685$
567.2-b4
567.2-b
$4$
$10$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
567.2
\( 3^{4} \cdot 7 \)
\( - 3^{12} \cdot 7 \)
$2.34819$
$(a-1), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B
$1$
\( 2 \)
$1$
$3.962390079$
0.367898682
\( \frac{94831363}{7} a + 24861195 \)
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -53 a - 131\) , \( 385 a + 824\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-53a-131\right){x}+385a+824$
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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.