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Elliptic curves over $\Q$ of conductor 575
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Conductor
prime
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CM discriminant -3
CM discriminant -4
CM discriminant -7
CM discriminant -8
CM discriminant -11
CM discriminant -12
CM discriminant -16
CM discriminant -19
CM discriminant -27
CM discriminant -28
CM discriminant -43
CM discriminant -67
CM discriminant -163
trivial
order 4
order 8
order 12
ℤ/2ℤ
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ℤ/2ℤ⊕ℤ/8ℤ
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✓ LMFDB curve label
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Label
Cremona label
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Cremona class
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Class degree
Conductor
Discriminant
Rank
Torsion
$\textrm{End}^0(E_{\overline\Q})$
CM
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$\ell$-adic images
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j-invariant
Weierstrass coefficients
Weierstrass equation
mod-$m$ images
MW-generators
575.a1
575e1
575.a
575e
$1$
$1$
\( 5^{2} \cdot 23 \)
\( - 5^{3} \cdot 23 \)
$1$
$\mathsf{trivial}$
$\Q$
$\mathrm{SU}(2)$
$230$
$2$
$0$
$0.091525914$
$1$
$10$
$56$
$-0.481710$
$-5451776/23$
$[0, 1, 1, -18, 24]$
\(y^2+y=x^3+x^2-18x+24\)
230.2.0.?
$[(3, 2)]$
575.b1
575b1
575.b
575b
$1$
$1$
\( 5^{2} \cdot 23 \)
\( - 5^{11} \cdot 23 \)
$1$
$\mathsf{trivial}$
$\Q$
$\mathrm{SU}(2)$
$230$
$2$
$0$
$0.347924568$
$1$
$4$
$240$
$0.421237$
$37933056/71875$
$[0, 0, 1, 175, -1344]$
\(y^2+y=x^3+175x-1344\)
230.2.0.?
$[(45, 312)]$
575.c1
575d1
575.c
575d
$1$
$1$
\( 5^{2} \cdot 23 \)
\( 5^{8} \cdot 23 \)
$1$
$\mathsf{trivial}$
$\Q$
$\mathrm{SU}(2)$
$92$
$2$
$0$
$0.229248300$
$1$
$6$
$60$
$0.027223$
$46305/23$
$[1, -1, 1, -55, 72]$
\(y^2+xy+y=x^3-x^2-55x+72\)
92.2.0.?
$[(-6, 15)]$
575.d1
575a1
575.d
575a
$1$
$1$
\( 5^{2} \cdot 23 \)
\( 5^{2} \cdot 23 \)
$1$
$\mathsf{trivial}$
$\Q$
$\mathrm{SU}(2)$
$92$
$2$
$0$
$0.517030746$
$1$
$2$
$12$
$-0.777496$
$46305/23$
$[1, -1, 0, -2, 1]$
\(y^2+xy=x^3-x^2-2x+1\)
92.2.0.?
$[(0, 1)]$
575.e1
575c1
575.e
575c
$1$
$1$
\( 5^{2} \cdot 23 \)
\( - 5^{9} \cdot 23 \)
$0$
$\mathsf{trivial}$
$\Q$
$\mathrm{SU}(2)$
$230$
$2$
$0$
$1$
$1$
$0$
$280$
$0.323009$
$-5451776/23$
$[0, -1, 1, -458, 3943]$
\(y^2+y=x^3-x^2-458x+3943\)
230.2.0.?
$[]$
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