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
145.3-a4
145.3-a
$8$
$12$
\(\Q(\zeta_{15})^+\)
$4$
$[4, 0]$
145.3
\( 5 \cdot 29 \)
\( 5^{6} \cdot 29^{6} \)
$5.58323$
$(-a-1), (-a^3+a^2+4a-2)$
0
$\Z/2\Z\oplus\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2Cs , 3B.1.1
$1$
\( 2^{2} \cdot 3^{2} \)
$1$
$169.1813275$
1.261003163
\( \frac{1583779420652621584630444}{14870583025} a^{3} + \frac{1309929568361659159883623}{14870583025} a^{2} - \frac{3941757265842103816828531}{14870583025} a - \frac{173366239902931707913796}{2974116605} \)
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - 3 a + 1\) , \( 7 a^{3} - 19 a^{2} - 86 a - 45\) , \( 353 a^{3} + 222 a^{2} - 980 a - 125\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(7a^{3}-19a^{2}-86a-45\right){x}+353a^{3}+222a^{2}-980a-125$
145.3-c6
145.3-c
$8$
$12$
\(\Q(\zeta_{15})^+\)
$4$
$[4, 0]$
145.3
\( 5 \cdot 29 \)
\( 5^{6} \cdot 29^{6} \)
$5.58323$
$(-a-1), (-a^3+a^2+4a-2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2Cs , 3B.1.2
$9$
\( 2^{2} \)
$1$
$14.42414881$
0.967601317
\( \frac{1583779420652621584630444}{14870583025} a^{3} + \frac{1309929568361659159883623}{14870583025} a^{2} - \frac{3941757265842103816828531}{14870583025} a - \frac{173366239902931707913796}{2974116605} \)
\( \bigl[a\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -946 a^{3} - 781 a^{2} + 2358 a + 508\) , \( -22779 a^{3} - 18841 a^{2} + 56695 a + 12461\bigr] \)
${y}^2+a{x}{y}+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(-946a^{3}-781a^{2}+2358a+508\right){x}-22779a^{3}-18841a^{2}+56695a+12461$
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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.