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
10.1-a1
10.1-a
$1$
$1$
\(\Q(\sqrt{46}) \)
$2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( - 2 \cdot 5^{3} \)
$2.15550$
$(-23a+156), (9a+61)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 3 \)
$0.298859460$
$19.55351800$
2.584843496
\( -\frac{59899811}{250} a + \frac{201658777}{125} \)
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 85 a - 555\) , \( 941 a - 6363\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(85a-555\right){x}+941a-6363$
10.1-b1
10.1-b
$1$
$1$
\(\Q(\sqrt{46}) \)
$2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( 2^{9} \cdot 5^{12} \)
$2.15550$
$(-23a+156), (9a+61)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3Ns
$1$
\( 2 \)
$1$
$5.798023056$
0.854871861
\( -\frac{13777032407}{7812500000} a - \frac{3369992913}{1953125000} \)
\( \bigl[1\) , \( 1\) , \( 0\) , \( -508516327 a - 3448925531\) , \( 183383033227434 a + 1243764244654883\bigr] \)
${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-508516327a-3448925531\right){x}+183383033227434a+1243764244654883$
10.1-c1
10.1-c
$1$
$1$
\(\Q(\sqrt{46}) \)
$2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( 2^{13} \cdot 5^{6} \)
$2.15550$
$(-23a+156), (9a+61)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$1$
$5.046478788$
0.744062704
\( -\frac{3776907459758737}{2000000} a - \frac{800507282019751}{62500} \)
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 1194937761 a - 8104462185\) , \( 202073642980310 a - 1370530127584686\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(1194937761a-8104462185\right){x}+202073642980310a-1370530127584686$
10.1-d1
10.1-d
$1$
$1$
\(\Q(\sqrt{46}) \)
$2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( 2^{13} \cdot 5^{6} \)
$2.15550$
$(-23a+156), (9a+61)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \cdot 3 \)
$2.527378401$
$1.362540458$
3.046435665
\( -\frac{3776907459758737}{2000000} a - \frac{800507282019751}{62500} \)
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -42 a - 232\) , \( -439 a - 2868\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-42a-232\right){x}-439a-2868$
10.1-e1
10.1-e
$1$
$1$
\(\Q(\sqrt{46}) \)
$2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( 2^{9} \cdot 5^{12} \)
$2.15550$
$(-23a+156), (9a+61)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3Ns
$1$
\( 2^{2} \cdot 3 \)
$0.996707357$
$1.919163130$
3.384401555
\( -\frac{13777032407}{7812500000} a - \frac{3369992913}{1953125000} \)
\( \bigl[1\) , \( 1\) , \( a\) , \( -a + 1\) , \( a - 41\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-a+1\right){x}+a-41$
10.1-f1
10.1-f
$1$
$1$
\(\Q(\sqrt{46}) \)
$2$
$[2, 0]$
10.1
\( 2 \cdot 5 \)
\( - 2 \cdot 5^{3} \)
$2.15550$
$(-23a+156), (9a+61)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$15.53590747$
1.145322294
\( -\frac{59899811}{250} a + \frac{201658777}{125} \)
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -1407458 a - 9545831\) , \( -2538606312 a - 17217665723\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1407458a-9545831\right){x}-2538606312a-17217665723$
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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.