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
1792.1-a2
1792.1-a
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
1792.1
\( 2^{8} \cdot 7 \)
\( 2^{15} \cdot 7^{3} \)
$1.53823$
$(a), (-2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3Cn
$1$
\( 2 \cdot 3 \)
$0.220380576$
$3.124709647$
1.561655422
\( -\frac{608715}{49} a + \frac{447714}{49} \)
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 2 a - 8\) , \( -a + 14\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a-8\right){x}-a+14$
1792.1-b2
1792.1-b
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
1792.1
\( 2^{8} \cdot 7 \)
\( 2^{9} \cdot 7^{3} \)
$1.53823$
$(a), (-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3Cn
$1$
\( 2 \)
$1$
$4.419006762$
1.670227562
\( -\frac{608715}{49} a + \frac{447714}{49} \)
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 2 a + 4\) , \( -4 a + 3\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a+4\right){x}-4a+3$
12544.1-b2
12544.1-b
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
12544.1
\( 2^{8} \cdot 7^{2} \)
\( 2^{9} \cdot 7^{9} \)
$2.50205$
$(a), (-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3Cn
$1$
\( 2^{2} \)
$1$
$1.670227562$
1.262573360
\( -\frac{608715}{49} a + \frac{447714}{49} \)
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -10 a - 18\) , \( -17 a - 22\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-10a-18\right){x}-17a-22$
12544.1-e2
12544.1-e
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
12544.1
\( 2^{8} \cdot 7^{2} \)
\( 2^{15} \cdot 7^{9} \)
$2.50205$
$(a), (-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3Cn
$1$
\( 2^{3} \)
$1$
$1.181029235$
1.785548370
\( -\frac{608715}{49} a + \frac{447714}{49} \)
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -7 a + 60\) , \( -124 a - 25\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-7a+60\right){x}-124a-25$
28672.5-d2
28672.5-d
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
28672.5
\( 2^{12} \cdot 7 \)
\( 2^{27} \cdot 7^{3} \)
$3.07647$
$(a), (-a+1), (-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3Cn
$1$
\( 2^{3} \)
$1$
$1.562354823$
2.362058470
\( -\frac{608715}{49} a + \frac{447714}{49} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -23 a + 2\) , \( 50 a - 44\bigr] \)
${y}^2={x}^{3}+\left(-23a+2\right){x}+50a-44$
28672.5-k2
28672.5-k
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
28672.5
\( 2^{12} \cdot 7 \)
\( 2^{21} \cdot 7^{3} \)
$3.07647$
$(a), (-a+1), (-2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3Cn
$1$
\( 2^{3} \cdot 3 \)
$0.240387146$
$2.209503381$
4.818014847
\( -\frac{608715}{49} a + \frac{447714}{49} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 11 a - 12\) , \( 18 a - 4\bigr] \)
${y}^2={x}^{3}+\left(11a-12\right){x}+18a-4$
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.