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
676.2-b2 676.2-b $5$
$9$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
676.2
\( 2^{2} \cdot 13^{2} \)
\( 2^{6} \cdot 13^{6} \)
$0.78920$
$(-4a+1), (4a-3), (2)$
0
$\Z/3\Z\oplus\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$3$
3Cs.1.1[2] $1$
\( 3^{3} \)
$1$
$2.690802392$
1.035690323
\( -\frac{10218313}{17576} \)
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -5 a + 4\) , \( -8\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-5a+4\right){x}-8$
8788.2-a2 8788.2-a $5$
$9$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
8788.2
\( 2^{2} \cdot 13^{3} \)
\( 2^{6} \cdot 13^{12} \)
$1.49855$
$(-4a+1), (4a-3), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3Cs[2] $1$
\( 2^{2} \)
$0.261585480$
$0.746294307$
1.803362851
\( -\frac{10218313}{17576} \)
\( \bigl[a\) , \( 1\) , \( 1\) , \( -32 a - 36\) , \( -279 a - 132\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-32a-36\right){x}-279a-132$
8788.3-a2 8788.3-a $5$
$9$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
8788.3
\( 2^{2} \cdot 13^{3} \)
\( 2^{6} \cdot 13^{12} \)
$1.49855$
$(-4a+1), (4a-3), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3Cs[2] $1$
\( 2^{2} \)
$0.261585480$
$0.746294307$
1.803362851
\( -\frac{10218313}{17576} \)
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 36 a + 31\) , \( 279 a - 411\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(36a+31\right){x}+279a-411$
43264.2-f2 43264.2-f $5$
$9$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
43264.2
\( 2^{8} \cdot 13^{2} \)
\( 2^{30} \cdot 13^{6} \)
$2.23219$
$(-4a+1), (4a-3), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3Cs[2] $1$
\( 2^{2} \cdot 3^{2} \)
$0.055429397$
$0.672700598$
3.100015278
\( -\frac{10218313}{17576} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -72\) , \( 496\bigr] \) ${y}^2={x}^{3}-{x}^{2}-72{x}+496$
114244.3-j2 114244.3-j $5$
$9$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
114244.3
\( 2^{2} \cdot 13^{4} \)
\( 2^{6} \cdot 13^{18} \)
$2.84549$
$(-4a+1), (4a-3), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3Cs[2] $1$
\( 2^{2} \cdot 3 \)
$1$
$0.206984799$
2.868065512
\( -\frac{10218313}{17576} \)
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -764 a + 764\) , \( -16264\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-764a+764\right){x}-16264$
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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.
