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
8.1-c2
8.1-c
$8$
$28$
3.3.961.1
$3$
$[3, 0]$
8.1
\( 2^{3} \)
\( 2^{42} \)
$3.91756$
$(-1/2a^2-1/2a+3), (-1/2a^2+1/2a+4), (a^2-11)$
0
$\Z/2\Z\oplus\Z/14\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 7$
2Cs , 7B.1.1
$1$
\( 2^{3} \cdot 7^{3} \)
$1$
$45.25275072$
5.109181533
\( \frac{42396561}{16384} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( \frac{12321}{2} a^{2} - \frac{2627}{2} a - 62639\) , \( -335922 a^{2} + 71618 a + 3415569\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(\frac{12321}{2}a^{2}-\frac{2627}{2}a-62639\right){x}-335922a^{2}+71618a+3415569$
39.1-b4
39.1-b
$8$
$28$
5.5.36497.1
$5$
$[5, 0]$
39.1
\( 3 \cdot 13 \)
\( 3^{14} \cdot 13^{2} \)
$24.62485$
$(a^2-1), (a^3-3a)$
0
$\Z/2\Z\oplus\Z/14\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 7$
2Cs , 7B.1.1
$1$
\( 2^{2} \cdot 7 \)
$1$
$8019.861435$
1.49927138
\( \frac{681363632760910}{808321761} a^{4} - \frac{50134304890058}{269440587} a^{3} - \frac{518208005828660}{269440587} a^{2} + \frac{361111060198751}{808321761} a + \frac{518784067066631}{808321761} \)
\( \bigl[a^{2} - a - 1\) , \( -a^{2} + a + 2\) , \( a^{2} - a - 1\) , \( 8 a^{4} - 20 a^{3} - 18 a^{2} + 50 a - 15\) , \( -5 a^{4} + 14 a^{3} + 10 a^{2} - 35 a + 12\bigr] \)
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(8a^{4}-20a^{3}-18a^{2}+50a-15\right){x}-5a^{4}+14a^{3}+10a^{2}-35a+12$
1.1-b5
1.1-b
$8$
$28$
6.6.722000.1
$6$
$[6, 0]$
1.1
\( 1 \)
\( 1 \)
$75.92891$
$\textsf{none}$
0
$\Z/2\Z\oplus\Z/14\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 7$
2Cs , 7B.1.1
$1$
\( 1 \)
$1$
$382987.4502$
0.574910
\( -278528 a^{5} + 139264 a^{4} + 1671168 a^{3} - 1114112 a^{2} - 1392640 a + 786432 \)
\( \bigl[0\) , \( 3 a^{5} - 2 a^{4} - 19 a^{3} + 14 a^{2} + 18 a - 8\) , \( -3 a^{5} + 2 a^{4} + 19 a^{3} - 14 a^{2} - 18 a + 8\) , \( a^{4} - a^{3} - 5 a^{2} + 7 a - 1\) , \( -a^{4} + a^{3} + 5 a^{2} - 7 a + 1\bigr] \)
${y}^2+\left(-3a^{5}+2a^{4}+19a^{3}-14a^{2}-18a+8\right){y}={x}^{3}+\left(3a^{5}-2a^{4}-19a^{3}+14a^{2}+18a-8\right){x}^{2}+\left(a^{4}-a^{3}-5a^{2}+7a-1\right){x}-a^{4}+a^{3}+5a^{2}-7a+1$
49.1-a4
49.1-a
$8$
$28$
\(\Q(\zeta_{28})^+\)
$6$
$[6, 0]$
49.1
\( 7^{2} \)
\( 7^{6} \)
$128.18090$
$(a^5-5a^3+5a)$
$0 \le r \le 1$
$\Z/2\Z\oplus\Z/14\Z$
$\textsf{potential}$
$-28$
$N(\mathrm{U}(1))$
✓
✓
✓
$2, 7$
2Cs , 7B.1.1[3]
\( 2^{2} \)
$1$
$125372.8339$
3.19416
\( 16581375 \)
\( \bigl[a^{4} - 4 a^{2} + 3\) , \( -a^{4} + 3 a^{2} + 1\) , \( a^{4} - 3 a^{2} + 1\) , \( -12 a^{4} + 73 a^{2} - 111\) , \( 27 a^{4} - 171 a^{2} + 258\bigr] \)
${y}^2+\left(a^{4}-4a^{2}+3\right){x}{y}+\left(a^{4}-3a^{2}+1\right){y}={x}^{3}+\left(-a^{4}+3a^{2}+1\right){x}^{2}+\left(-12a^{4}+73a^{2}-111\right){x}+27a^{4}-171a^{2}+258$
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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.