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
17.4-a1 17.4-a $2$
$2$
4.4.17069.1 $4$
$[4, 0]$
17.4
\( 17 \)
\( 17 \)
$16.63599$
$(-a^3+2a^2+4a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 1 \)
$1$
$488.6817180$
0.935108622
\( -\frac{64103}{17} a^{3} - \frac{654046}{17} a^{2} + \frac{1325795}{17} a + \frac{3860476}{17} \)
\( \bigl[a^{2} - 2 a - 3\) , \( -a^{3} + 2 a^{2} + 6 a + 1\) , \( a^{3} - a^{2} - 6 a - 4\) , \( -2 a^{3} + 5 a^{2} + 7 a - 2\) , \( -2 a^{3} + 6 a^{2} + 3 a - 9\bigr] \) ${y}^2+\left(a^{2}-2a-3\right){x}{y}+\left(a^{3}-a^{2}-6a-4\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+6a+1\right){x}^{2}+\left(-2a^{3}+5a^{2}+7a-2\right){x}-2a^{3}+6a^{2}+3a-9$
17.4-a2 17.4-a $2$
$2$
4.4.17069.1 $4$
$[4, 0]$
17.4
\( 17 \)
\( - 17^{2} \)
$16.63599$
$(-a^3+2a^2+4a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2 \)
$1$
$244.3408590$
0.935108622
\( \frac{571484617685}{289} a^{3} - \frac{914174258472}{289} a^{2} - \frac{2559358195393}{289} a + \frac{1156480881791}{289} \)
\( \bigl[a^{2} - 2 a - 3\) , \( -a^{3} + 2 a^{2} + 6 a + 1\) , \( a^{3} - a^{2} - 6 a - 4\) , \( 8 a^{3} - 25 a^{2} - 28 a + 18\) , \( -16 a^{3} + 33 a^{2} + 42 a - 27\bigr] \) ${y}^2+\left(a^{2}-2a-3\right){x}{y}+\left(a^{3}-a^{2}-6a-4\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+6a+1\right){x}^{2}+\left(8a^{3}-25a^{2}-28a+18\right){x}-16a^{3}+33a^{2}+42a-27$
17.4-b1 17.4-b $1$
$1$
4.4.17069.1 $4$
$[4, 0]$
17.4
\( 17 \)
\( 17 \)
$16.63599$
$(-a^3+2a^2+4a-1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$1$
\( 1 \)
$0.071860716$
$1427.519210$
3.140721722
\( \frac{2871}{17} a^{3} - \frac{10257}{17} a^{2} - \frac{3833}{17} a + \frac{15684}{17} \)
\( \bigl[a^{3} - a^{2} - 6 a - 4\) , \( a^{3} - 3 a^{2} - 2 a + 5\) , \( a + 1\) , \( -7 a^{3} + 8 a^{2} + 60 a + 49\) , \( -9 a^{3} + 10 a^{2} + 87 a + 75\bigr] \) ${y}^2+\left(a^{3}-a^{2}-6a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-3a^{2}-2a+5\right){x}^{2}+\left(-7a^{3}+8a^{2}+60a+49\right){x}-9a^{3}+10a^{2}+87a+75$
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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.
