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
5.1-a3
5.1-a
$4$
$15$
6.6.1241125.1
$6$
$[6, 0]$
5.1
\( 5 \)
\( 5^{5} \)
$113.83972$
$(-2a^5+a^4+13a^3-2a^2-19a-5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3, 5$
3B , 5B.4.1[2]
$1$
\( 1 \)
$1$
$1682.101420$
1.50989
\( -\frac{13681459876}{125} a^{5} - \frac{36187576902}{125} a^{4} + \frac{25331233773}{125} a^{3} + \frac{99876956003}{125} a^{2} + \frac{10695502109}{25} a + \frac{7259236048}{125} \)
\( \bigl[-5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 52 a - 19\) , \( -2 a^{5} + 13 a^{3} + 3 a^{2} - 19 a - 7\) , \( a^{2} + a - 2\) , \( 20 a^{5} - 9 a^{4} - 145 a^{3} + 8 a^{2} + 244 a + 98\) , \( 13 a^{5} - 7 a^{4} - 106 a^{3} - 6 a^{2} + 200 a + 114\bigr] \)
${y}^2+\left(-5a^{5}+2a^{4}+34a^{3}-2a^{2}-52a-19\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-2a^{5}+13a^{3}+3a^{2}-19a-7\right){x}^{2}+\left(20a^{5}-9a^{4}-145a^{3}+8a^{2}+244a+98\right){x}+13a^{5}-7a^{4}-106a^{3}-6a^{2}+200a+114$
25.2-b3
25.2-b
$4$
$15$
6.6.1241125.1
$6$
$[6, 0]$
25.2
\( 5^{2} \)
\( 5^{11} \)
$130.17912$
$(-2a^5+a^4+13a^3-2a^2-19a-5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3, 5$
3B , 5B.1.4[2]
$25$
\( 2 \)
$1$
$40.42142472$
1.81415
\( -\frac{13681459876}{125} a^{5} - \frac{36187576902}{125} a^{4} + \frac{25331233773}{125} a^{3} + \frac{99876956003}{125} a^{2} + \frac{10695502109}{25} a + \frac{7259236048}{125} \)
\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} - a^{2} - 23 a - 10\) , \( 4 a^{5} - a^{4} - 28 a^{3} - a^{2} + 45 a + 16\) , \( -5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 53 a - 18\) , \( 4 a^{5} - a^{4} - 48 a^{3} - 8 a^{2} + 139 a + 64\) , \( 5 a^{5} + 11 a^{4} - 60 a^{3} - 66 a^{2} + 162 a + 80\bigr] \)
${y}^2+\left(-2a^{5}+a^{4}+14a^{3}-a^{2}-23a-10\right){x}{y}+\left(-5a^{5}+2a^{4}+34a^{3}-2a^{2}-53a-18\right){y}={x}^{3}+\left(4a^{5}-a^{4}-28a^{3}-a^{2}+45a+16\right){x}^{2}+\left(4a^{5}-a^{4}-48a^{3}-8a^{2}+139a+64\right){x}+5a^{5}+11a^{4}-60a^{3}-66a^{2}+162a+80$
405.2-m3
405.2-m
$4$
$15$
6.6.1241125.1
$6$
$[6, 0]$
405.2
\( 3^{4} \cdot 5 \)
\( 3^{12} \cdot 5^{5} \)
$164.18529$
$(-2a^5+a^4+13a^3-2a^2-19a-5), (2a^5-a^4-14a^3+2a^2+23a+6)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$3, 5$
3B.1.1 , 5B.4.1[2]
$1$
\( 1 \)
$1$
$8255.689373$
0.823385
\( -\frac{13681459876}{125} a^{5} - \frac{36187576902}{125} a^{4} + \frac{25331233773}{125} a^{3} + \frac{99876956003}{125} a^{2} + \frac{10695502109}{25} a + \frac{7259236048}{125} \)
\( \bigl[-4 a^{5} + 2 a^{4} + 27 a^{3} - 4 a^{2} - 41 a - 12\) , \( -a^{3} + a^{2} + 5 a - 2\) , \( -4 a^{5} + 2 a^{4} + 27 a^{3} - 4 a^{2} - 42 a - 13\) , \( -9 a^{5} - 5 a^{4} + 54 a^{3} + 38 a^{2} - 51 a - 35\) , \( -63 a^{5} + 16 a^{4} + 417 a^{3} - 4 a^{2} - 598 a - 155\bigr] \)
${y}^2+\left(-4a^{5}+2a^{4}+27a^{3}-4a^{2}-41a-12\right){x}{y}+\left(-4a^{5}+2a^{4}+27a^{3}-4a^{2}-42a-13\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-2\right){x}^{2}+\left(-9a^{5}-5a^{4}+54a^{3}+38a^{2}-51a-35\right){x}-63a^{5}+16a^{4}+417a^{3}-4a^{2}-598a-155$
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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.