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
145.3-a7 145.3-a $8$
$12$
\(\Q(\zeta_{15})^+\) $4$
$[4, 0]$
145.3
\( 5 \cdot 29 \)
\( 5 \cdot 29 \)
$5.58323$
$(-a-1), (-a^3+a^2+4a-2)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2, 3$
2B , 3B.1.2 $1$
\( 1 \)
$1$
$676.7253102$
1.261003163
\( -\frac{451821}{145} a^{3} - \frac{571893}{145} a^{2} + \frac{1829142}{145} a + \frac{1322804}{145} \)
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - 3 a + 1\) , \( 2 a^{3} + a^{2} - 6 a\) , \( 7 a^{3} + 3 a^{2} - 24 a - 6\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(2a^{3}+a^{2}-6a\right){x}+7a^{3}+3a^{2}-24a-6$
145.3-c1 145.3-c $8$
$12$
\(\Q(\zeta_{15})^+\) $4$
$[4, 0]$
145.3
\( 5 \cdot 29 \)
\( 5 \cdot 29 \)
$5.58323$
$(-a-1), (-a^3+a^2+4a-2)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2, 3$
2B , 3B.1.1 $1$
\( 1 \)
$1$
$1168.356053$
0.967601317
\( -\frac{451821}{145} a^{3} - \frac{571893}{145} a^{2} + \frac{1829142}{145} a + \frac{1322804}{145} \)
\( \bigl[a\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -a^{3} - a^{2} + 3 a + 3\) , \( -3 a^{3} - 2 a^{2} + 8 a + 1\bigr] \) ${y}^2+a{x}{y}+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-a^{3}-a^{2}+3a+3\right){x}-3a^{3}-2a^{2}+8a+1$
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Pari/GP
SageMath
Magma
Oscar
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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.
