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-a3 45.1-a $10$
$32$
\(\Q(\zeta_{15})^+\) $4$
$[4, 0]$
45.1
\( 3^{2} \cdot 5 \)
\( 3^{8} \cdot 5^{8} \)
$4.82355$
$(-a-1), (-a^3+a^2+3a-2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2$
2Cs $1$
\( 2^{2} \)
$1$
$103.8759859$
0.774245886
\( \frac{13997521}{225} \)
\( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{3} + a^{2} + 4 a - 3\) , \( a^{3} + a^{2} - 2 a - 1\) , \( 5 a^{3} - 26 a^{2} + 20 a + 8\) , \( 32 a^{3} - 129 a^{2} + 96 a + 25\bigr] \) ${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-3\right){x}^{2}+\left(5a^{3}-26a^{2}+20a+8\right){x}+32a^{3}-129a^{2}+96a+25$
45.1-b8 45.1-b $10$
$32$
\(\Q(\zeta_{15})^+\) $4$
$[4, 0]$
45.1
\( 3^{2} \cdot 5 \)
\( 3^{8} \cdot 5^{8} \)
$4.82355$
$(-a-1), (-a^3+a^2+3a-2)$
0
$\Z/2\Z\oplus\Z/16\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2$
2Cs $1$
\( 2^{5} \)
$1$
$985.1451572$
0.917854808
\( \frac{13997521}{225} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5{x}+2$
Download
displayed columns for
to
Text
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.
