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
3136.4-a1
3136.4-a
$1$
$1$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
3136.4
\( 2^{6} \cdot 7^{2} \)
\( 2^{8} \cdot 7^{8} \)
$1.76922$
$(a), (-a+1), (-2a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cn
$1$
\( 2^{2} \cdot 3 \)
$0.071541228$
$2.124947498$
2.758016206
\( 12544 \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -16\) , \( 29\bigr] \)
${y}^2={x}^{3}-{x}^{2}-16{x}+29$
6272.4-b1
6272.4-b
$1$
$1$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
6272.4
\( 2^{7} \cdot 7^{2} \)
\( 2^{8} \cdot 7^{2} \)
$2.10397$
$(a), (-a+1), (-2a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cn
$1$
\( 2 \)
$0.182292284$
$5.622082628$
3.098892262
\( 12544 \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 2\) , \( -1\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}-1$
6272.5-b1
6272.5-b
$1$
$1$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
6272.5
\( 2^{7} \cdot 7^{2} \)
\( 2^{8} \cdot 7^{2} \)
$2.10397$
$(a), (-a+1), (-2a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cn
$1$
\( 2 \)
$0.182292284$
$5.622082628$
3.098892262
\( 12544 \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 2\) , \( 1\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+2\right){x}+1$
12544.5-a1
12544.5-a
$1$
$1$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
12544.5
\( 2^{8} \cdot 7^{2} \)
\( 2^{8} \cdot 7^{8} \)
$2.50205$
$(a), (-a+1), (-2a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cn
$1$
\( 1 \)
$1.004255008$
$2.124947498$
3.226288365
\( 12544 \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -16\) , \( -29\bigr] \)
${y}^2={x}^{3}+{x}^{2}-16{x}-29$
25088.4-m1
25088.4-m
$1$
$1$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
25088.4
\( 2^{9} \cdot 7^{2} \)
\( 2^{14} \cdot 7^{2} \)
$2.97546$
$(a), (-a+1), (-2a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cn
$1$
\( 2 \)
$0.385152047$
$3.975412751$
4.629727225
\( 12544 \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2 a - 5\) , \( 4 a - 3\bigr] \)
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a-5\right){x}+4a-3$
25088.4-n1
25088.4-n
$1$
$1$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
25088.4
\( 2^{9} \cdot 7^{2} \)
\( 2^{14} \cdot 7^{8} \)
$2.97546$
$(a), (-a+1), (-2a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cn
$1$
\( 2 \)
$1$
$1.502564785$
2.271664429
\( 12544 \)
\( \bigl[0\) , \( a\) , \( 0\) , \( -16 a + 32\) , \( 29 a + 58\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+\left(-16a+32\right){x}+29a+58$
25088.7-m1
25088.7-m
$1$
$1$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
25088.7
\( 2^{9} \cdot 7^{2} \)
\( 2^{14} \cdot 7^{2} \)
$2.97546$
$(a), (-a+1), (-2a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cn
$1$
\( 2 \)
$0.385152047$
$3.975412751$
4.629727225
\( 12544 \)
\( \bigl[0\) , \( a\) , \( 0\) , \( -2 a - 3\) , \( -4 a + 1\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+\left(-2a-3\right){x}-4a+1$
25088.7-n1
25088.7-n
$1$
$1$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
25088.7
\( 2^{9} \cdot 7^{2} \)
\( 2^{14} \cdot 7^{8} \)
$2.97546$
$(a), (-a+1), (-2a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cn
$1$
\( 2 \)
$1$
$1.502564785$
2.271664429
\( 12544 \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 16 a + 16\) , \( -29 a + 87\bigr] \)
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(16a+16\right){x}-29a+87$
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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.