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
100.1-c4
100.1-c
$4$
$6$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
100.1
\( 2^{2} \cdot 5^{2} \)
\( 2^{6} \cdot 5^{4} \)
$1.29494$
$(-a), (-a+1), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$0.403882379$
$9.768635228$
1.721904841
\( \frac{8527173507}{200} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 42 a - 128\) , \( 261 a - 718\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(42a-128\right){x}+261a-718$
100.1-f4
100.1-f
$4$
$6$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
100.1
\( 2^{2} \cdot 5^{2} \)
\( 2^{6} \cdot 5^{4} \)
$1.29494$
$(-a), (-a+1), (2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$0.403882379$
$9.768635228$
1.721904841
\( \frac{8527173507}{200} \)
\( \bigl[a\) , \( -1\) , \( 1\) , \( -43 a - 85\) , \( -261 a - 457\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-43a-85\right){x}-261a-457$
900.1-k4
900.1-k
$4$
$6$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
900.1
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \)
\( 2^{6} \cdot 3^{6} \cdot 5^{4} \)
$2.24289$
$(-a+2), (-a), (-a+1), (2)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{3} \cdot 3 \)
$1$
$15.76958961$
2.294137716
\( \frac{8527173507}{200} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -128\) , \( 587\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-128{x}+587$
900.1-p4
900.1-p
$4$
$6$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
900.1
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \)
\( 2^{6} \cdot 3^{6} \cdot 5^{4} \)
$2.24289$
$(-a+2), (-a), (-a+1), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2^{3} \cdot 3 \)
$1$
$2.017094010$
2.640995995
\( \frac{8527173507}{200} \)
\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 637 a - 1785\) , \( 14094 a - 39346\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(637a-1785\right){x}+14094a-39346$
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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.