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
26.1-a1 26.1-a $2$
$3$
3.3.148.1 $3$
$[3, 0]$
26.1
\( 2 \cdot 13 \)
\( - 2 \cdot 13 \)
$1.87111$
$(a^2-a-2), (a^2-2a-2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3B.1.1 $1$
\( 1 \)
$1$
$83.69718755$
0.764429604
\( \frac{47519}{26} a^{2} - \frac{15283}{13} a - \frac{161671}{26} \)
\( \bigl[1\) , \( a^{2} - 2 a - 3\) , \( a^{2} - 2\) , \( -a^{2} + 4\) , \( -a - 1\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(-a^{2}+4\right){x}-a-1$
26.1-a2 26.1-a $2$
$3$
3.3.148.1 $3$
$[3, 0]$
26.1
\( 2 \cdot 13 \)
\( - 2^{3} \cdot 13^{3} \)
$1.87111$
$(a^2-a-2), (a^2-2a-2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3B.1.2 $1$
\( 3 \)
$1$
$3.099895835$
0.764429604
\( -\frac{936828579535}{4394} a^{2} + \frac{1669497916531}{4394} a - \frac{428712816945}{4394} \)
\( \bigl[1\) , \( a^{2} - 2 a - 3\) , \( a^{2} - 2\) , \( -26 a^{2} - 25 a + 19\) , \( -93 a^{2} - 111 a + 36\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(-26a^{2}-25a+19\right){x}-93a^{2}-111a+36$
26.1-b1 26.1-b $2$
$7$
3.3.148.1 $3$
$[3, 0]$
26.1
\( 2 \cdot 13 \)
\( - 2 \cdot 13^{7} \)
$1.87111$
$(a^2-a-2), (a^2-2a-2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$7$
7B.1.3 $49$
\( 1 \)
$1$
$0.292786373$
1.179277689
\( \frac{2930762217049733062408935}{125497034} a^{2} - \frac{1009489594983775464711535}{62748517} a - \frac{9420406871887862637780499}{125497034} \)
\( \bigl[1\) , \( a^{2} - a - 1\) , \( a\) , \( -412332 a^{2} - 482491 a + 189971\) , \( -265768689 a^{2} - 310972408 a + 122469086\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(-412332a^{2}-482491a+189971\right){x}-265768689a^{2}-310972408a+122469086$
26.1-b2 26.1-b $2$
$7$
3.3.148.1 $3$
$[3, 0]$
26.1
\( 2 \cdot 13 \)
\( - 2^{7} \cdot 13 \)
$1.87111$
$(a^2-a-2), (a^2-2a-2)$
0
$\Z/7\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$7$
7B.1.1 $1$
\( 7 \)
$1$
$100.4257259$
1.179277689
\( -\frac{192290305}{104} a^{2} + \frac{119296865}{26} a - \frac{129845369}{104} \)
\( \bigl[1\) , \( -a^{2} + 1\) , \( a + 1\) , \( a^{2} - 2\) , \( 20 a^{2} - 15 a - 66\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+1\right){x}^{2}+\left(a^{2}-2\right){x}+20a^{2}-15a-66$
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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.
