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
104.1-a1
104.1-a
$2$
$7$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
104.1
\( 2^{3} \cdot 13 \)
\( - 2^{21} \cdot 13^{7} \)
$1.35647$
$(a^2+a-3), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B.1.6[3]
$1$
\( 7 \)
$1$
$0.693240326$
0.693240326
\( -\frac{244166998716801995}{4015905088} a^{2} + \frac{274090208021491107}{2007952544} a - \frac{391207563784495951}{8031810176} \)
\( \bigl[a\) , \( -a - 1\) , \( a^{2} - 2\) , \( -40 a^{2} - 10 a\) , \( -150 a^{2} - 66 a + 6\bigr] \)
${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-40a^{2}-10a\right){x}-150a^{2}-66a+6$
104.1-a2
104.1-a
$2$
$7$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
104.1
\( 2^{3} \cdot 13 \)
\( - 2^{3} \cdot 13 \)
$1.35647$
$(a^2+a-3), (2)$
0
$\Z/7\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B.1.1[3]
$1$
\( 1 \)
$1$
$237.7814320$
0.693240326
\( \frac{209979}{13} a^{2} - \frac{245189}{26} a - \frac{460974}{13} \)
\( \bigl[a\) , \( -a - 1\) , \( a^{2} - 2\) , \( 0\) , \( 0\bigr] \)
${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a-1\right){x}^{2}$
104.1-b1
104.1-b
$3$
$9$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
104.1
\( 2^{3} \cdot 13 \)
\( - 2^{27} \cdot 13^{3} \)
$1.35647$
$(a^2+a-3), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$9$
\( 3 \)
$1$
$0.173437023$
0.668971376
\( \frac{10376980113762479800901}{1124864} a^{2} - \frac{179962171805350369053}{35152} a - \frac{23316862668979013718273}{1124864} \)
\( \bigl[a^{2} + a - 1\) , \( a^{2} - 3\) , \( a^{2} - 1\) , \( 559 a^{2} + 571 a - 2847\) , \( 9577 a^{2} + 11912 a - 52573\bigr] \)
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(559a^{2}+571a-2847\right){x}+9577a^{2}+11912a-52573$
104.1-b2
104.1-b
$3$
$9$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
104.1
\( 2^{3} \cdot 13 \)
\( - 2^{9} \cdot 13^{9} \)
$1.35647$
$(a^2+a-3), (2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3Cs.1.1
$1$
\( 3^{2} \)
$1$
$4.682799632$
0.668971376
\( \frac{5104794835848393}{42417997492} a^{2} - \frac{5647619780915441}{84835994984} a - \frac{5729473372444955}{21208998746} \)
\( \bigl[a^{2} + a - 1\) , \( a^{2} - 3\) , \( a^{2} - 1\) , \( 14 a^{2} - 9 a - 27\) , \( -28 a^{2} + 93 a - 74\bigr] \)
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(14a^{2}-9a-27\right){x}-28a^{2}+93a-74$
104.1-b3
104.1-b
$3$
$9$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
104.1
\( 2^{3} \cdot 13 \)
\( - 2^{3} \cdot 13^{3} \)
$1.35647$
$(a^2+a-3), (2)$
0
$\Z/9\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 3 \)
$1$
$126.4355900$
0.668971376
\( -\frac{96759805}{2197} a^{2} - \frac{153935551}{4394} a + \frac{108957411}{4394} \)
\( \bigl[a^{2} + a - 1\) , \( a^{2} - 3\) , \( a^{2} - 1\) , \( -a^{2} + a + 3\) , \( 3 a^{2} - 4 a - 1\bigr] \)
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-a^{2}+a+3\right){x}+3a^{2}-4a-1$
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.