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
75.1-a2 75.1-a $8$
$16$
\(\Q(\sqrt{-33}) \) $2$
$[0, 1]$
75.1
\( 3 \cdot 5^{2} \)
\( 3^{14} \cdot 5^{2} \)
$3.02128$
$(3,a), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2$
2Cs $1$
\( 2 \)
$4.497953220$
$8.942806850$
7.002156534
\( -\frac{1}{15} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( 0\) , \( -5\bigr] \) ${y}^2+{x}{y}={x}^3-{x}^2-5$
75.1-b2 75.1-b $8$
$16$
\(\Q(\sqrt{-33}) \) $2$
$[0, 1]$
75.1
\( 3 \cdot 5^{2} \)
\( 3^{14} \cdot 5^{2} \)
$3.02128$
$(3,a), (5)$
$2$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2$
2Cs $1$
\( 2 \)
$2.166417365$
$8.942806850$
6.745109504
\( -\frac{1}{15} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( 39\) , \( -7\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+39{x}-7$
75.1-c2 75.1-c $8$
$16$
\(\Q(\sqrt{-33}) \) $2$
$[0, 1]$
75.1
\( 3 \cdot 5^{2} \)
\( 3^{2} \cdot 5^{2} \)
$3.02128$
$(3,a), (5)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2$
2Cs $4$
\( 2 \)
$1$
$8.942806850$
0.778371427
\( -\frac{1}{15} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2$
75.1-d2 75.1-d $8$
$16$
\(\Q(\sqrt{-33}) \) $2$
$[0, 1]$
75.1
\( 3 \cdot 5^{2} \)
\( 3^{2} \cdot 5^{2} \)
$3.02128$
$(3,a), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2$
2Cs $1$
\( 2 \)
$2.338219894$
$8.942806850$
3.640007112
\( -\frac{1}{15} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( 34\) , \( -6\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+34{x}-6$
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Pari/GP
SageMath
Magma
Oscar
CSV
*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.
