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
50700.3-a1 50700.3-a $1$
$1$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
50700.3
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \)
\( 2^{10} \cdot 3^{11} \cdot 5^{4} \cdot 13^{8} \)
$2.32248$
$(-2a+1), (4a-3), (2), (5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $1$
\( 2 \)
$1$
$0.301248308$
0.695703166
\( \frac{46880677}{291600} a + \frac{205902887}{583200} \)
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 386 a - 127\) , \( -4431 a + 3411\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(386a-127\right){x}-4431a+3411$
50700.3-c1 50700.3-c $1$
$1$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
50700.3
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \)
\( 2^{10} \cdot 3^{11} \cdot 5^{4} \cdot 13^{2} \)
$2.32248$
$(-2a+1), (4a-3), (2), (5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $1$
\( 2 \cdot 5 \cdot 11 \)
$0.015980506$
$1.086166221$
4.409393735
\( \frac{46880677}{291600} a + \frac{205902887}{583200} \)
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -22 a - 7\) , \( -51 a + 99\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-22a-7\right){x}-51a+99$
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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.
