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
10.1-a3
10.1-a
$6$
$8$
3.3.733.1
$3$
$[3, 0]$
10.1
\( 2 \cdot 5 \)
\( 2^{2} \cdot 5^{4} \)
$3.55105$
$(a^2-6), (-a+3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$252.0026523$
2.326982585
\( \frac{255581}{2500} a^{2} - \frac{8033}{2500} a + \frac{4266969}{2500} \)
\( \bigl[1\) , \( -a\) , \( a^{2} - 4\) , \( -793533281 a^{2} - 1204741195 a + 2520955258\) , \( 11680631678321 a^{2} + 17733519821337 a - 37107895199680\bigr] \)
${y}^2+{x}{y}+\left(a^{2}-4\right){y}={x}^{3}-a{x}^{2}+\left(-793533281a^{2}-1204741195a+2520955258\right){x}+11680631678321a^{2}+17733519821337a-37107895199680$
50.2-c1
50.2-c
$6$
$8$
3.3.733.1
$3$
$[3, 0]$
50.2
\( 2 \cdot 5^{2} \)
\( 2^{2} \cdot 5^{10} \)
$4.64357$
$(a^2-6), (-a+3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$89.83913051$
1.659141999
\( \frac{255581}{2500} a^{2} - \frac{8033}{2500} a + \frac{4266969}{2500} \)
\( \bigl[a^{2} - 5\) , \( -a\) , \( a^{2} + a - 4\) , \( -244029 a^{2} - 370486 a + 775250\) , \( 63156416 a^{2} + 95883988 a - 200639976\bigr] \)
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}+a-4\right){y}={x}^{3}-a{x}^{2}+\left(-244029a^{2}-370486a+775250\right){x}+63156416a^{2}+95883988a-200639976$
80.3-a3
80.3-a
$6$
$8$
3.3.733.1
$3$
$[3, 0]$
80.3
\( 2^{4} \cdot 5 \)
\( 2^{14} \cdot 5^{4} \)
$5.02195$
$(a^2-6), (-a+3)$
$1$
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{4} \)
$1.326573545$
$107.4777561$
3.949655339
\( \frac{255581}{2500} a^{2} - \frac{8033}{2500} a + \frac{4266969}{2500} \)
\( \bigl[a^{2} + a - 4\) , \( -a\) , \( a\) , \( -44 a^{2} - 67 a + 141\) , \( 101 a^{2} + 154 a - 322\bigr] \)
${y}^2+\left(a^{2}+a-4\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-44a^{2}-67a+141\right){x}+101a^{2}+154a-322$
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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.