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
145.3-a8
145.3-a
$8$
$12$
\(\Q(\zeta_{15})^+\)
$4$
$[4, 0]$
145.3
\( 5 \cdot 29 \)
\( 5^{12} \cdot 29^{12} \)
$5.58323$
$(-a-1), (-a^3+a^2+4a-2)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{4} \cdot 3^{2} \)
$1$
$10.57383297$
1.261003163
\( \frac{234852755657943296835935447}{44226847900683630125} a^{3} + \frac{39101078088251811097507079}{8845369580136726025} a^{2} - \frac{585878518549436834574701384}{44226847900683630125} a - \frac{128887630498703941143525046}{44226847900683630125} \)
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - 3 a + 1\) , \( -358 a^{3} - 149 a^{2} + 1214 a + 240\) , \( -301 a^{3} - 19 a^{2} + 1354 a + 404\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-358a^{3}-149a^{2}+1214a+240\right){x}-301a^{3}-19a^{2}+1354a+404$
145.3-c7
145.3-c
$8$
$12$
\(\Q(\zeta_{15})^+\)
$4$
$[4, 0]$
145.3
\( 5 \cdot 29 \)
\( 5^{12} \cdot 29^{12} \)
$5.58323$
$(-a-1), (-a^3+a^2+4a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.2
$9$
\( 2^{2} \)
$1$
$3.606037203$
0.967601317
\( \frac{234852755657943296835935447}{44226847900683630125} a^{3} + \frac{39101078088251811097507079}{8845369580136726025} a^{2} - \frac{585878518549436834574701384}{44226847900683630125} a - \frac{128887630498703941143525046}{44226847900683630125} \)
\( \bigl[a\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -951 a^{3} - 801 a^{2} + 2403 a + 523\) , \( -22813 a^{3} - 18780 a^{2} + 56708 a + 12443\bigr] \)
${y}^2+a{x}{y}+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-951a^{3}-801a^{2}+2403a+523\right){x}-22813a^{3}-18780a^{2}+56708a+12443$
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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.