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
74.4-a1 74.4-a $2$
$3$
\(\Q(\sqrt{73}) \) $2$
$[2, 0]$
74.4
\( 2 \cdot 37 \)
\( 2 \cdot 37^{6} \)
$2.23928$
$(a+4), (2a+5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3B.1.2 $1$
\( 2 \cdot 3 \)
$1$
$2.324532616$
1.632395784
\( -\frac{1656100646297}{5131452818} a - \frac{3173087208905}{5131452818} \)
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -2234 a + 10670\) , \( 161836 a - 772266\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-2234a+10670\right){x}+161836a-772266$
74.4-a2 74.4-a $2$
$3$
\(\Q(\sqrt{73}) \) $2$
$[2, 0]$
74.4
\( 2 \cdot 37 \)
\( 2^{3} \cdot 37^{2} \)
$2.23928$
$(a+4), (2a+5)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3B.1.1 $1$
\( 2 \cdot 3 \)
$1$
$20.92079354$
1.632395784
\( \frac{2467951}{10952} a + \frac{560575}{10952} \)
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 266 a - 1260\) , \( -8433 a + 40258\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(266a-1260\right){x}-8433a+40258$
74.4-b1 74.4-b $1$
$1$
\(\Q(\sqrt{73}) \) $2$
$[2, 0]$
74.4
\( 2 \cdot 37 \)
\( - 2^{8} \cdot 37 \)
$2.23928$
$(a+4), (2a+5)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$1$
\( 2 \)
$0.044517945$
$27.44376363$
1.143950773
\( -\frac{7592207}{9472} a - \frac{9342047}{9472} \)
\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -2 a + 1\) , \( -a + 1\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a+1\right){x}-a+1$
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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.
