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
7.1-b2
7.1-b
$6$
$8$
3.3.733.1
$3$
$[3, 0]$
7.1
\( 7 \)
\( 7 \)
$3.34611$
$(a^2+2a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$64$
\( 1 \)
$1$
$1.433724702$
0.847293282
\( -\frac{84096891433574753384471}{7} a^{2} - \frac{14985568201611275023622}{7} a + \frac{571022332294137577763767}{7} \)
\( \bigl[a^{2} - 5\) , \( a^{2} - a - 5\) , \( 1\) , \( 28 a^{2} + 141 a - 533\) , \( -38 a^{2} + 1741 a - 4144\bigr] \)
${y}^2+\left(a^{2}-5\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(28a^{2}+141a-533\right){x}-38a^{2}+1741a-4144$
49.2-a4
49.2-a
$6$
$8$
3.3.733.1
$3$
$[3, 0]$
49.2
\( 7^{2} \)
\( 7^{7} \)
$4.62796$
$(a^2+2a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$64$
\( 2 \)
$1$
$1.831258952$
2.164450966
\( -\frac{84096891433574753384471}{7} a^{2} - \frac{14985568201611275023622}{7} a + \frac{571022332294137577763767}{7} \)
\( \bigl[1\) , \( -a^{2} + 6\) , \( 1\) , \( -10 a^{2} + 174 a - 367\) , \( 747 a^{2} - 2047 a + 127\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-10a^{2}+174a-367\right){x}+747a^{2}-2047a+127$
112.3-d4
112.3-d
$6$
$8$
3.3.733.1
$3$
$[3, 0]$
112.3
\( 2^{4} \cdot 7 \)
\( 2^{12} \cdot 7 \)
$5.31162$
$(a^2-6), (a^2+2a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$16$
\( 2^{2} \)
$1$
$2.422527886$
1.431649745
\( -\frac{84096891433574753384471}{7} a^{2} - \frac{14985568201611275023622}{7} a + \frac{571022332294137577763767}{7} \)
\( \bigl[a\) , \( a^{2} - 5\) , \( a^{2} - 4\) , \( 318 a^{2} + 457 a - 1072\) , \( -167802 a^{2} - 254825 a + 532900\bigr] \)
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(318a^{2}+457a-1072\right){x}-167802a^{2}-254825a+532900$
175.2-c4
175.2-c
$6$
$8$
3.3.733.1
$3$
$[3, 0]$
175.2
\( 5^{2} \cdot 7 \)
\( 5^{6} \cdot 7 \)
$5.72177$
$(-a+3), (a^2+2a-3)$
$2$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$1.191330722$
$18.10045343$
3.584118192
\( -\frac{84096891433574753384471}{7} a^{2} - \frac{14985568201611275023622}{7} a + \frac{571022332294137577763767}{7} \)
\( \bigl[a + 1\) , \( a^{2} + a - 4\) , \( a^{2} + a - 4\) , \( 24 a^{2} + 52 a - 250\) , \( -245 a^{2} - 473 a + 1667\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(24a^{2}+52a-250\right){x}-245a^{2}-473a+1667$
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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.