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
4.1-a1
4.1-a
$2$
$2$
3.3.733.1
$3$
$[3, 0]$
4.1
\( 2^{2} \)
\( 2^{2} \)
$3.04813$
$(a^2+a-3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$0.169949645$
$211.0086285$
0.993412807
\( -\frac{2179161}{2} a^{2} - \frac{980655}{2} a + 8146597 \)
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -249848597 a^{2} - 379319816 a + 793737515\) , \( 2203418510276 a^{2} + 3345227116373 a - 6999982998532\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-249848597a^{2}-379319816a+793737515\right){x}+2203418510276a^{2}+3345227116373a-6999982998532$
64.3-b2
64.3-b
$2$
$2$
3.3.733.1
$3$
$[3, 0]$
64.3
\( 2^{6} \)
\( 2^{14} \)
$4.83861$
$(a^2-6), (a^2+a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$46.51537529$
1.718084587
\( -\frac{2179161}{2} a^{2} - \frac{980655}{2} a + 8146597 \)
\( \bigl[a^{2} + a - 4\) , \( -a^{2} + 4\) , \( 0\) , \( -14 a^{2} - 19 a + 45\) , \( 12 a^{2} + 19 a - 38\bigr] \)
${y}^2+\left(a^{2}+a-4\right){x}{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-14a^{2}-19a+45\right){x}+12a^{2}+19a-38$
100.3-a1
100.3-a
$2$
$2$
3.3.733.1
$3$
$[3, 0]$
100.3
\( 2^{2} \cdot 5^{2} \)
\( 2^{2} \cdot 5^{6} \)
$5.21223$
$(-a+3), (a^2+a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$1$
$103.4059361$
1.909692699
\( -\frac{2179161}{2} a^{2} - \frac{980655}{2} a + 8146597 \)
\( \bigl[a^{2} - 5\) , \( -a^{2} - a + 5\) , \( 1\) , \( -76836 a^{2} - 116649 a + 244107\) , \( 11970733 a^{2} + 18173953 a - 38029506\bigr] \)
${y}^2+\left(a^{2}-5\right){x}{y}+{y}={x}^{3}+\left(-a^{2}-a+5\right){x}^{2}+\left(-76836a^{2}-116649a+244107\right){x}+11970733a^{2}+18173953a-38029506$
196.3-e2
196.3-e
$2$
$2$
3.3.733.1
$3$
$[3, 0]$
196.3
\( 2^{2} \cdot 7^{2} \)
\( 2^{2} \cdot 7^{6} \)
$5.83087$
$(a^2+2a-3), (a^2+a-3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$2.315071552$
$35.16231862$
4.510048322
\( -\frac{2179161}{2} a^{2} - \frac{980655}{2} a + 8146597 \)
\( \bigl[a + 1\) , \( -a^{2} - a + 6\) , \( a^{2} - 5\) , \( -17535930466 a^{2} - 26623026823 a + 55709441748\) , \( 1295696859035729 a^{2} + 1967125286109270 a - 4116265676357783\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(-17535930466a^{2}-26623026823a+55709441748\right){x}+1295696859035729a^{2}+1967125286109270a-4116265676357783$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.