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
15.4-a1
15.4-a
$2$
$3$
\(\Q(\sqrt{301}) \)
$2$
$[2, 0]$
15.4
\( 3 \cdot 5 \)
\( 3^{2} \cdot 5^{6} \)
$3.05102$
$(-a-8), (6a+49)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 2^{2} \)
$1$
$18.93354958$
4.365246621
\( -\frac{24051712}{140625} a - \frac{1933312}{1875} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -90938 a + 834327\) , \( -84627209 a + 776427205\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}+\left(-90938a+834327\right){x}-84627209a+776427205$
15.4-a2
15.4-a
$2$
$3$
\(\Q(\sqrt{301}) \)
$2$
$[2, 0]$
15.4
\( 3 \cdot 5 \)
\( 3^{6} \cdot 5^{2} \)
$3.05102$
$(-a-8), (6a+49)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 2^{2} \)
$1$
$18.93354958$
4.365246621
\( \frac{403177472}{18225} a - \frac{49020928}{243} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( 1910572 a + 15618307\) , \( -2687078497 a - 21965995526\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}+\left(1910572a+15618307\right){x}-2687078497a-21965995526$
15.4-b1
15.4-b
$2$
$3$
\(\Q(\sqrt{301}) \)
$2$
$[2, 0]$
15.4
\( 3 \cdot 5 \)
\( 3^{2} \cdot 5^{6} \)
$3.05102$
$(-a-8), (6a+49)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 2^{2} \cdot 3 \)
$1$
$5.384850921$
3.724531766
\( -\frac{24051712}{140625} a - \frac{1933312}{1875} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( -42 a - 343\) , \( -577 a - 4717\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}+\left(-42a-343\right){x}-577a-4717$
15.4-b2
15.4-b
$2$
$3$
\(\Q(\sqrt{301}) \)
$2$
$[2, 0]$
15.4
\( 3 \cdot 5 \)
\( 3^{6} \cdot 5^{2} \)
$3.05102$
$(-a-8), (6a+49)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 2^{2} \cdot 3 \)
$1$
$5.384850921$
3.724531766
\( \frac{403177472}{18225} a - \frac{49020928}{243} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( 8 a - 73\) , \( 39 a - 358\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}+\left(8a-73\right){x}+39a-358$
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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.