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
41.2-a2
41.2-a
$2$
$7$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
41.2
\( 41 \)
\( 41 \)
$0.50561$
$(a-7)$
0
$\Z/7\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B.1.1
$1$
\( 1 \)
$1$
$46.26087846$
0.422214159
\( \frac{176128}{41} a - \frac{286720}{41} \)
\( \bigl[0\) , \( \phi - 1\) , \( \phi + 1\) , \( 0\) , \( -\phi\bigr] \)
${y}^2+\left(\phi+1\right){y}={x}^{3}+\left(\phi-1\right){x}^{2}-\phi$
1025.2-a2
1025.2-a
$2$
$7$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
1025.2
\( 5^{2} \cdot 41 \)
\( 5^{6} \cdot 41 \)
$1.13059$
$(-2a+1), (a-7)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$7$
7B.6.1
$1$
\( 1 \)
$1$
$3.626679053$
1.621900179
\( \frac{176128}{41} a - \frac{286720}{41} \)
\( \bigl[0\) , \( \phi + 1\) , \( \phi + 1\) , \( \phi - 1\) , \( -3 \phi - 3\bigr] \)
${y}^2+\left(\phi+1\right){y}={x}^{3}+\left(\phi+1\right){x}^{2}+\left(\phi-1\right){x}-3\phi-3$
1681.2-b2
1681.2-b
$2$
$7$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
1681.2
\( 41^{2} \)
\( 41^{7} \)
$1.27943$
$(a-7)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$7$
7B.6.1
$1$
\( 2 \)
$1$
$1.266491262$
1.132784221
\( \frac{176128}{41} a - \frac{286720}{41} \)
\( \bigl[0\) , \( 1\) , \( \phi + 1\) , \( -8 \phi - 12\) , \( -141 \phi - 98\bigr] \)
${y}^2+\left(\phi+1\right){y}={x}^{3}+{x}^{2}+\left(-8\phi-12\right){x}-141\phi-98$
3321.2-f2
3321.2-f
$2$
$7$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
3321.2
\( 3^{4} \cdot 41 \)
\( 3^{12} \cdot 41 \)
$1.51684$
$(a-7), (3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$7$
7B.6.1
$1$
\( 2 \)
$0.432983079$
$2.703166965$
2.093720884
\( \frac{176128}{41} a - \frac{286720}{41} \)
\( \bigl[0\) , \( 0\) , \( \phi + 1\) , \( 3 \phi - 6\) , \( 2 \phi - 8\bigr] \)
${y}^2+\left(\phi+1\right){y}={x}^{3}+\left(3\phi-6\right){x}+2\phi-8$
4961.3-e2
4961.3-e
$2$
$7$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
4961.3
\( 11^{2} \cdot 41 \)
\( 11^{6} \cdot 41 \)
$1.67693$
$(-3a+2), (a-7)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$7$
7B.6.1
$1$
\( 1 \)
$1$
$4.738782752$
2.119248073
\( \frac{176128}{41} a - \frac{286720}{41} \)
\( \bigl[0\) , \( \phi - 1\) , \( \phi + 1\) , \( 5 \phi - 9\) , \( 6 \phi - 9\bigr] \)
${y}^2+\left(\phi+1\right){y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(5\phi-9\right){x}+6\phi-9$
4961.5-f2
4961.5-f
$2$
$7$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
4961.5
\( 11^{2} \cdot 41 \)
\( 11^{6} \cdot 41 \)
$1.67693$
$(-3a+1), (a-7)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$7$
7B.6.1
$1$
\( 2 \)
$0.235455977$
$7.196950528$
3.031330060
\( \frac{176128}{41} a - \frac{286720}{41} \)
\( \bigl[0\) , \( \phi - 1\) , \( \phi + 1\) , \( 2 \phi - 5\) , \( -9 \phi + 6\bigr] \)
${y}^2+\left(\phi+1\right){y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(2\phi-5\right){x}-9\phi+6$
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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.