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
45.1-b7
45.1-b
$8$
$16$
\(\Q(\sqrt{205}) \)
$2$
$[2, 0]$
45.1
\( 3^{2} \cdot 5 \)
\( 3^{2} \cdot 5^{2} \)
$3.31374$
$(3,a), (3,a+2), (a+7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2 \)
$2.706065934$
$31.38702211$
5.932142254
\( \frac{56667352321}{15} \)
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -10316 a - 68672\) , \( 1463000 a + 9742005\bigr] \)
${y}^2+\left(w+1\right){x}{y}={x}^3+\left(-10316w-68672\right){x}+1463000w+9742005$
45.1-c7
45.1-c
$8$
$16$
\(\Q(\sqrt{205}) \)
$2$
$[2, 0]$
45.1
\( 3^{2} \cdot 5 \)
\( 3^{2} \cdot 5^{2} \)
$3.31374$
$(3,a), (3,a+2), (a+7)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2 \)
$4.300387515$
$31.38702211$
2.356789441
\( \frac{56667352321}{15} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \)
${y}^2+{x}{y}+{y}={x}^3+{x}^2-80{x}+242$
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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.