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
\( -\frac{244166998716801995}{4015905088} a^{2} + \frac{274090208021491107}{2007952544} a - \frac{391207563784495951}{8031810176} \)
\( \bigl[a\) , \( -a - 1\) , \( a^{2} - 2\) , \( -40 a^{2} - 10 a\) , \( -150 a^{2} - 66 a + 6\bigr] \)
${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-40a^{2}-10a\right){x}-150a^{2}-66a+6$
1352.6-d2
1352.6-d
$2$
$7$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
1352.6
\( 2^{3} \cdot 13^{2} \)
\( - 2^{21} \cdot 13^{13} \)
$2.08001$
$(a^2+a-3), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$7$
7B.6.1[3]
$1$
\( 2^{2} \)
$0.222370955$
$4.556314713$
1.736900668
\( -\frac{244166998716801995}{4015905088} a^{2} + \frac{274090208021491107}{2007952544} a - \frac{391207563784495951}{8031810176} \)
\( \bigl[1\) , \( -a^{2} - a + 3\) , \( 0\) , \( -590 a^{2} - 152 a + 172\) , \( 9692 a^{2} + 5044 a - 4244\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-590a^{2}-152a+172\right){x}+9692a^{2}+5044a-4244$
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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.