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
152.1-a1
152.1-a
$1$
$1$
\(\Q(\sqrt{19}) \)
$2$
$[2, 0]$
152.1
\( 2^{3} \cdot 19 \)
\( 2^{4} \cdot 19^{2} \)
$2.73531$
$(-3a+13), (a)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$1$
\( 2^{2} \)
$1.166536130$
$6.946863007$
7.436526327
\( -\frac{1024}{19} \)
\( \bigl[0\) , \( -1\) , \( a + 1\) , \( 4420 a - 19266\) , \( 1918754 a - 8363662\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(4420a-19266\right){x}+1918754a-8363662$
152.1-b1
152.1-b
$1$
$1$
\(\Q(\sqrt{19}) \)
$2$
$[2, 0]$
152.1
\( 2^{3} \cdot 19 \)
\( 2^{10} \cdot 19^{2} \)
$2.73531$
$(-3a+13), (a)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$1$
\( 2^{2} \)
$1$
$3.737734601$
1.714990253
\( -\frac{31250}{19} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 27629 a - 120395\) , \( 7448822 a - 32468619\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(27629a-120395\right){x}+7448822a-32468619$
152.1-c1
152.1-c
$1$
$1$
\(\Q(\sqrt{19}) \)
$2$
$[2, 0]$
152.1
\( 2^{3} \cdot 19 \)
\( 2^{10} \cdot 19^{2} \)
$2.73531$
$(-3a+13), (a)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$1$
\( 2^{2} \)
$0.100262567$
$22.71038060$
4.179038978
\( -\frac{31250}{19} \)
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 27630 a - 120392\) , \( -7486350 a + 32632300\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(27630a-120392\right){x}-7486350a+32632300$
152.1-d1
152.1-d
$1$
$1$
\(\Q(\sqrt{19}) \)
$2$
$[2, 0]$
152.1
\( 2^{3} \cdot 19 \)
\( 2^{4} \cdot 19^{2} \)
$2.73531$
$(-3a+13), (a)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$1$
\( 2^{2} \)
$0.065414869$
$26.58148262$
1.595654537
\( -\frac{1024}{19} \)
\( \bigl[0\) , \( 1\) , \( a + 1\) , \( 4420 a - 19266\) , \( -1918755 a + 8363652\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(4420a-19266\right){x}-1918755a+8363652$
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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.