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
29.2-a1 29.2-a $2$
$7$
4.4.5125.1 $4$
$[4, 0]$
29.2
\( 29 \)
\( -29 \)
$9.74508$
$(a^2-6)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$7$
7B.6.1 $1$
\( 1 \)
$1$
$125.2260233$
1.749232970
\( -\frac{1067314607}{29} a^{3} + \frac{3332543358}{29} a^{2} + \frac{2663592680}{29} a - \frac{10460703482}{29} \)
\( \bigl[a^{3} - 5 a - 3\) , \( -a\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -2 a^{3} + 3 a^{2} + 6 a - 7\) , \( -2 a^{3} + 4 a^{2} + 6 a - 12\bigr] \) ${y}^2+\left(a^{3}-5a-3\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}-a{x}^{2}+\left(-2a^{3}+3a^{2}+6a-7\right){x}-2a^{3}+4a^{2}+6a-12$
29.2-b1 29.2-b $2$
$7$
4.4.5125.1 $4$
$[4, 0]$
29.2
\( 29 \)
\( -29 \)
$9.74508$
$(a^2-6)$
$1$
$\Z/7\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$7$
7B.1.1 $1$
\( 1 \)
$1.056492173$
$1661.600912$
2.001750670
\( -\frac{1067314607}{29} a^{3} + \frac{3332543358}{29} a^{2} + \frac{2663592680}{29} a - \frac{10460703482}{29} \)
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{3} - 4 a - 3\) , \( 2 a^{3} - a^{2} - 11 a - 6\) , \( -5 a^{3} - a^{2} + 27 a + 24\bigr] \) ${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{3}-4a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(2a^{3}-a^{2}-11a-6\right){x}-5a^{3}-a^{2}+27a+24$
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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.
