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
64.1-a1
64.1-a
$1$
$1$
6.6.703493.1
$6$
$[6, 0]$
64.1
\( 2^{6} \)
\( - 2^{6} \)
$105.99453$
$(2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$1363.207533$
1.62530
\( 146989275419572 a^{5} - \frac{143700390471519}{2} a^{4} - 843525494076395 a^{3} + \frac{684313694606955}{2} a^{2} + 811041701707335 a - \frac{194534795299797}{2} \)
\( \bigl[a^{5} - 6 a^{3} + 8 a + 1\) , \( -a^{5} + a^{4} + 6 a^{3} - 5 a^{2} - 7 a + 2\) , \( a^{5} - a^{4} - 6 a^{3} + 5 a^{2} + 7 a - 1\) , \( -4 a^{5} + 2 a^{4} + 23 a^{3} - 12 a^{2} - 22 a + 3\) , \( -7 a^{5} + 4 a^{4} + 39 a^{3} - 20 a^{2} - 41 a + 5\bigr] \)
${y}^2+\left(a^{5}-6a^{3}+8a+1\right){x}{y}+\left(a^{5}-a^{4}-6a^{3}+5a^{2}+7a-1\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-5a^{2}-7a+2\right){x}^{2}+\left(-4a^{5}+2a^{4}+23a^{3}-12a^{2}-22a+3\right){x}-7a^{5}+4a^{4}+39a^{3}-20a^{2}-41a+5$
64.1-b1
64.1-b
$1$
$1$
6.6.703493.1
$6$
$[6, 0]$
64.1
\( 2^{6} \)
\( - 2^{18} \)
$105.99453$
$(2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 3 \)
$0.007393886$
$19202.85666$
3.04706
\( -\frac{4155719}{8} a^{5} - \frac{2581671}{8} a^{4} + \frac{16657899}{8} a^{3} + \frac{900641}{4} a^{2} - 1374892 a + \frac{1236175}{8} \)
\( \bigl[a^{5} - a^{4} - 6 a^{3} + 5 a^{2} + 6 a - 1\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 10 a^{2} + 2 a - 5\) , \( a^{5} - a^{4} - 5 a^{3} + 6 a^{2} + 3 a - 3\) , \( a^{5} + 2 a^{4} - 6 a^{3} - 13 a^{2} + 7 a + 18\) , \( -11 a^{5} + 2 a^{4} + 64 a^{3} - 8 a^{2} - 66 a - 8\bigr] \)
${y}^2+\left(a^{5}-a^{4}-6a^{3}+5a^{2}+6a-1\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+6a^{2}+3a-3\right){y}={x}^{3}+\left(a^{5}-2a^{4}-5a^{3}+10a^{2}+2a-5\right){x}^{2}+\left(a^{5}+2a^{4}-6a^{3}-13a^{2}+7a+18\right){x}-11a^{5}+2a^{4}+64a^{3}-8a^{2}-66a-8$
64.1-c1
64.1-c
$1$
$1$
6.6.703493.1
$6$
$[6, 0]$
64.1
\( 2^{6} \)
\( - 2^{18} \)
$105.99453$
$(2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 3 \)
$0.007393886$
$19202.85666$
3.04706
\( 1361559 a^{5} - 2557565 a^{4} - \frac{57078417}{8} a^{3} + \frac{113409673}{8} a^{2} + 4389277 a - \frac{94213565}{8} \)
\( \bigl[a^{5} - a^{4} - 6 a^{3} + 5 a^{2} + 6 a - 1\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 4\) , \( 3 a^{5} - 2 a^{4} - 17 a^{3} + 11 a^{2} + 16 a - 4\) , \( 2 a^{4} - 9 a^{2} + 3 a + 6\) , \( -2 a^{4} + 4 a^{3} + 8 a^{2} - 17 a + 4\bigr] \)
${y}^2+\left(a^{5}-a^{4}-6a^{3}+5a^{2}+6a-1\right){x}{y}+\left(3a^{5}-2a^{4}-17a^{3}+11a^{2}+16a-4\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+4a+4\right){x}^{2}+\left(2a^{4}-9a^{2}+3a+6\right){x}-2a^{4}+4a^{3}+8a^{2}-17a+4$
64.1-d1
64.1-d
$1$
$1$
6.6.703493.1
$6$
$[6, 0]$
64.1
\( 2^{6} \)
\( - 2^{6} \)
$105.99453$
$(2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$1363.207533$
1.62530
\( -\frac{20074120848835}{2} a^{5} + 29671853291873 a^{4} + 21812204105468 a^{3} - 131265137584045 a^{2} + 105445461314860 a - 10496500642032 \)
\( \bigl[2 a^{5} - a^{4} - 12 a^{3} + 5 a^{2} + 14 a\) , \( -a^{5} + 5 a^{3} - 4 a - 1\) , \( a^{5} - 6 a^{3} + a^{2} + 7 a\) , \( -2 a^{4} + 10 a^{2} - 2 a - 10\) , \( -2 a^{4} + a^{3} + 9 a^{2} - 3 a - 9\bigr] \)
${y}^2+\left(2a^{5}-a^{4}-12a^{3}+5a^{2}+14a\right){x}{y}+\left(a^{5}-6a^{3}+a^{2}+7a\right){y}={x}^{3}+\left(-a^{5}+5a^{3}-4a-1\right){x}^{2}+\left(-2a^{4}+10a^{2}-2a-10\right){x}-2a^{4}+a^{3}+9a^{2}-3a-9$
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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.