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
2500.3-a4
2500.3-a
$4$
$15$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
2500.3
\( 2^{2} \cdot 5^{4} \)
\( 2^{30} \cdot 5^{4} \)
$2.09566$
$(-a-1), (a-2), (2)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3, 5$
3B , 5B.1.1
$1$
\( 3 \cdot 5 \)
$1$
$1.424166746$
0.515282916
\( \frac{46969655}{32768} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( 22\) , \( -9\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+22{x}-9$
2500.3-b4
2500.3-b
$4$
$15$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
2500.3
\( 2^{2} \cdot 5^{4} \)
\( 2^{30} \cdot 5^{10} \)
$2.09566$
$(-a-1), (a-2), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3, 5$
3B , 5B.4.1
$1$
\( 3 \)
$1$
$0.636906731$
1.152207629
\( \frac{46969655}{32768} \)
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( 64 a - 43\) , \( -102 a + 142\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(64a-43\right){x}-102a+142$
2500.3-d4
2500.3-d
$4$
$15$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
2500.3
\( 2^{2} \cdot 5^{4} \)
\( 2^{30} \cdot 5^{10} \)
$2.09566$
$(-a-1), (a-2), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3, 5$
3B , 5B.4.1
$1$
\( 3 \)
$1$
$0.636906731$
1.152207629
\( \frac{46969655}{32768} \)
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -67 a + 20\) , \( 56 a + 238\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-67a+20\right){x}+56a+238$
2500.3-h4
2500.3-h
$4$
$15$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
2500.3
\( 2^{2} \cdot 5^{4} \)
\( 2^{30} \cdot 5^{16} \)
$2.09566$
$(-a-1), (a-2), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3, 5$
3B.1.2 , 5B.1.4
$1$
\( 3 \cdot 5 \)
$1$
$0.284833349$
2.576414584
\( \frac{46969655}{32768} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( 549\) , \( -2202\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+549{x}-2202$
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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.