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
16.1-a12 16.1-a $12$
$24$
\(\Q(\sqrt{2}, \sqrt{5})\) $4$
$[4, 0]$
16.1
\( 2^{4} \)
\( 2^{16} \)
$5.05491$
$(1/2a^3-2a)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2, 3$
2Cs , 3B $1$
\( 1 \)
$1$
$533.1660961$
0.833072025
\( -30720 a^{3} + 245760 a + 204800 \)
\( \bigl[0\) , \( -\frac{1}{2} a^{3} + 3 a\) , \( 0\) , \( -4 a^{3} + 3 a^{2} + 22 a - 18\) , \( 12 a^{3} - 10 a^{2} - 64 a + 55\bigr] \) ${y}^2={x}^{3}+\left(-\frac{1}{2}a^{3}+3a\right){x}^{2}+\left(-4a^{3}+3a^{2}+22a-18\right){x}+12a^{3}-10a^{2}-64a+55$
256.1-a6 256.1-a $12$
$24$
\(\Q(\sqrt{2}, \sqrt{5})\) $4$
$[4, 0]$
256.1
\( 2^{8} \)
\( 2^{16} \)
$7.14872$
$(1/2a^3-2a)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2, 3$
2Cs , 3B $1$
\( 1 \)
$1$
$748.5646885$
1.169632325
\( -30720 a^{3} + 245760 a + 204800 \)
\( \bigl[0\) , \( \frac{1}{2} a^{3} - 2 a\) , \( 0\) , \( -a^{3} + 8 a - 6\) , \( -4 a^{3} + 5 a^{2} + 16 a - 15\bigr] \) ${y}^2={x}^{3}+\left(\frac{1}{2}a^{3}-2a\right){x}^{2}+\left(-a^{3}+8a-6\right){x}-4a^{3}+5a^{2}+16a-15$
256.1-e11 256.1-e $12$
$24$
\(\Q(\sqrt{2}, \sqrt{5})\) $4$
$[4, 0]$
256.1
\( 2^{8} \)
\( 2^{16} \)
$7.14872$
$(1/2a^3-2a)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2, 3$
2Cs , 3B $1$
\( 2^{2} \)
$1$
$1050.984105$
1.642162665
\( -30720 a^{3} + 245760 a + 204800 \)
\( \bigl[0\) , \( \frac{1}{2} a^{3} - 3 a\) , \( 0\) , \( -4 a^{3} + 3 a^{2} + 22 a - 18\) , \( -12 a^{3} + 10 a^{2} + 64 a - 55\bigr] \) ${y}^2={x}^{3}+\left(\frac{1}{2}a^{3}-3a\right){x}^{2}+\left(-4a^{3}+3a^{2}+22a-18\right){x}-12a^{3}+10a^{2}+64a-55$
256.1-f7 256.1-f $12$
$24$
\(\Q(\sqrt{2}, \sqrt{5})\) $4$
$[4, 0]$
256.1
\( 2^{8} \)
\( 2^{16} \)
$7.14872$
$(1/2a^3-2a)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2, 3$
2Cs , 3B $1$
\( 1 \)
$1$
$748.5646885$
1.169632325
\( -30720 a^{3} + 245760 a + 204800 \)
\( \bigl[0\) , \( -\frac{1}{2} a^{3} + 2 a\) , \( 0\) , \( -a^{3} + 8 a - 6\) , \( 4 a^{3} - 5 a^{2} - 16 a + 15\bigr] \) ${y}^2={x}^{3}+\left(-\frac{1}{2}a^{3}+2a\right){x}^{2}+\left(-a^{3}+8a-6\right){x}+4a^{3}-5a^{2}-16a+15$
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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.
