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
1225.2-a3 1225.2-a $5$
$9$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
1225.2
\( 5^{2} \cdot 7^{2} \)
\( 5^{6} \cdot 7^{6} \)
$0.91566$
$(-3a+1), (3a-2), (5)$
0
$\Z/3\Z\oplus\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$3$
3Cs.1.1[2] $1$
\( 3^{3} \)
$1$
$2.324925606$
0.894864283
\( \frac{71991296}{42875} \)
\( \bigl[0\) , \( -a\) , \( 1\) , \( 9 a - 9\) , \( 1\bigr] \) ${y}^2+{y}={x}^{3}-a{x}^{2}+\left(9a-9\right){x}+1$
30625.2-a3 30625.2-a $5$
$9$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
30625.2
\( 5^{4} \cdot 7^{2} \)
\( 5^{18} \cdot 7^{6} \)
$2.04747$
$(-3a+1), (3a-2), (5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3Cs[2] $1$
\( 2^{2} \)
$0.277720001$
$0.464985121$
1.192904208
\( \frac{71991296}{42875} \)
\( \bigl[0\) , \( a\) , \( 1\) , \( 217 a - 217\) , \( -282\bigr] \) ${y}^2+{y}={x}^{3}+a{x}^{2}+\left(217a-217\right){x}-282$
60025.3-b3 60025.3-b $5$
$9$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
60025.3
\( 5^{2} \cdot 7^{4} \)
\( 5^{6} \cdot 7^{18} \)
$2.42260$
$(-3a+1), (3a-2), (5)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$3$
3Cs[2] $1$
\( 2^{4} \cdot 3 \)
$0.041403129$
$0.332132229$
3.048700687
\( \frac{71991296}{42875} \)
\( \bigl[0\) , \( a\) , \( 1\) , \( 425 a - 425\) , \( 433\bigr] \) ${y}^2+{y}={x}^{3}+a{x}^{2}+\left(425a-425\right){x}+433$
77175.2-k3 77175.2-k $5$
$9$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
77175.2
\( 3^{2} \cdot 5^{2} \cdot 7^{3} \)
\( 3^{6} \cdot 5^{6} \cdot 7^{12} \)
$2.57969$
$(-2a+1), (-3a+1), (3a-2), (5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3Cs[2] $1$
\( 2 \cdot 3 \)
$1$
$0.507340360$
3.514957126
\( \frac{71991296}{42875} \)
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 209 a - 130\) , \( -5 a + 73\bigr] \) ${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(209a-130\right){x}-5a+73$
77175.3-k3 77175.3-k $5$
$9$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
77175.3
\( 3^{2} \cdot 5^{2} \cdot 7^{3} \)
\( 3^{6} \cdot 5^{6} \cdot 7^{12} \)
$2.57969$
$(-2a+1), (-3a+1), (3a-2), (5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$3$
3Cs[2] $1$
\( 2 \cdot 3 \)
$1$
$0.507340360$
3.514957126
\( \frac{71991296}{42875} \)
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -207 a + 78\) , \( 213 a - 10\bigr] \) ${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-207a+78\right){x}+213a-10$
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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.
