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-b1
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
\( \frac{960431553635305495}{7} a^{2} - \frac{3550132253411453690}{7} a + \frac{2849530108248409337}{7} \)
\( \bigl[a^{2} - 5\) , \( a^{2} - a - 5\) , \( 1\) , \( -572 a^{2} + 2121 a - 1723\) , \( -25034 a^{2} + 92549 a - 74316\bigr] \)
${y}^2+\left(a^{2}-5\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-572a^{2}+2121a-1723\right){x}-25034a^{2}+92549a-74316$
49.2-a3
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
$16$
\( 2^{2} \)
$1$
$3.662517904$
2.164450966
\( \frac{960431553635305495}{7} a^{2} - \frac{3550132253411453690}{7} a + \frac{2849530108248409337}{7} \)
\( \bigl[1\) , \( -a^{2} + 6\) , \( 1\) , \( -810 a^{2} + 2544 a - 1877\) , \( 33127 a^{2} - 126707 a + 103271\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-810a^{2}+2544a-1877\right){x}+33127a^{2}-126707a+103271$
112.3-d6
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
$16$
\( 2 \)
$1$
$4.845055773$
1.431649745
\( \frac{960431553635305495}{7} a^{2} - \frac{3550132253411453690}{7} a + \frac{2849530108248409337}{7} \)
\( \bigl[a\) , \( a^{2} - 5\) , \( a^{2} - 4\) , \( -22052 a^{2} - 33473 a + 70048\) , \( -3353096 a^{2} - 5090675 a + 10652372\bigr] \)
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-22052a^{2}-33473a+70048\right){x}-3353096a^{2}-5090675a+10652372$
175.2-c6
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
\( \frac{960431553635305495}{7} a^{2} - \frac{3550132253411453690}{7} a + \frac{2849530108248409337}{7} \)
\( \bigl[a + 1\) , \( a^{2} + a - 4\) , \( a^{2} + a - 4\) , \( -386 a^{2} + 312 a + 160\) , \( 29 a^{2} - 20035 a + 23577\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-386a^{2}+312a+160\right){x}+29a^{2}-20035a+23577$
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Pari/GP
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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.