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
15.1-a1
15.1-a
$2$
$3$
\(\Q(\sqrt{301}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 3^{6} \cdot 5^{2} \)
$3.05102$
$(-a+9), (-6a+55)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 2^{2} \)
$1$
$18.93354958$
4.365246621
\( -\frac{403177472}{18225} a - \frac{3273392128}{18225} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -1910572 a + 17528879\) , \( 2687078497 a - 24653074023\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}+\left(-1910572a+17528879\right){x}+2687078497a-24653074023$
15.1-b1
15.1-b
$2$
$3$
\(\Q(\sqrt{301}) \)
$2$
$[2, 0]$
15.1
\( 3 \cdot 5 \)
\( 3^{6} \cdot 5^{2} \)
$3.05102$
$(-a+9), (-6a+55)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 2^{2} \cdot 3 \)
$1$
$5.384850921$
3.724531766
\( -\frac{403177472}{18225} a - \frac{3273392128}{18225} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( -8 a - 65\) , \( -39 a - 319\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}+\left(-8a-65\right){x}-39a-319$
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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.