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
1.1-a2 1.1-a $4$
$15$
\(\Q(\sqrt{229}) \) $2$
$[2, 0]$
1.1
\( 1 \)
\( 3^{12} \)
$1.35225$
$\textsf{none}$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2, 3, 5$
2Cn , 3B.1.1 , 5B $9$
\( 1 \)
$1$
$38.58216293$
2.549581091
\( -888615 a + 7334137 \)
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( a - 3\) , \( 2 a + 6\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(a-3\right){x}+2a+6$
9.2-a2 9.2-a $4$
$15$
\(\Q(\sqrt{229}) \) $2$
$[2, 0]$
9.2
\( 3^{2} \)
\( 3^{6} \)
$2.34216$
$(3,a)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2, 3, 5$
2Cn , 3B , 5B $1$
\( 1 \)
$0.572385991$
$42.60204606$
3.222787782
\( -888615 a + 7334137 \)
\( \bigl[a\) , \( a\) , \( a\) , \( 23 a - 21\) , \( -a + 523\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(23a-21\right){x}-a+523$
9.3-a2 9.3-a $4$
$15$
\(\Q(\sqrt{229}) \) $2$
$[2, 0]$
9.3
\( 3^{2} \)
\( 3^{18} \)
$2.34216$
$(3,a+2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2, 3, 5$
2Cn , 3B , 5B $1$
\( 1 \)
$2.861929958$
$8.520409212$
3.222787782
\( -888615 a + 7334137 \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -9336 a - 65972\) , \( -1341295 a - 9478091\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-9336a-65972\right){x}-1341295a-9478091$
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Pari/GP
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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.
