Show commands: SageMath
Rank
The elliptic curves in class 45570.cr have rank \(1\).
L-function data
Bad L-factors: |
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Good L-factors: |
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See L-function page for more information |
Complex multiplication
The elliptic curves in class 45570.cr do not have complex multiplication.Modular form 45570.2.a.cr
Isogeny matrix
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
The vertices are labelled with LMFDB labels.
Elliptic curves in class 45570.cr
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
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45570.cr1 | 45570da6 | \([1, 0, 0, -601055561, 5671691591691]\) | \(204117072508351537504018561/1958536333827640350\) | \(230419841138488059537150\) | \([2]\) | \(15728640\) | \(3.6446\) | |
45570.cr2 | 45570da4 | \([1, 0, 0, -129015531, -564034181355]\) | \(2018651992700195476824481/75097045898437500\) | \(8835092352905273437500\) | \([2]\) | \(7864320\) | \(3.2980\) | |
45570.cr3 | 45570da3 | \([1, 0, 0, -38449811, 84228846141]\) | \(53434051027037036566561/4869932476018522500\) | \(572942685871103153602500\) | \([2, 2]\) | \(7864320\) | \(3.2980\) | |
45570.cr4 | 45570da2 | \([1, 0, 0, -8437311, -7951546359]\) | \(564608806599700366561/94616222006250000\) | \(11131503902813306250000\) | \([2, 2]\) | \(3932160\) | \(2.9514\) | |
45570.cr5 | 45570da1 | \([1, 0, 0, 974609, -702485575]\) | \(870215264126076959/2316066449760000\) | \(-272482901747814240000\) | \([2]\) | \(1966080\) | \(2.6048\) | \(\Gamma_0(N)\)-optimal |
45570.cr6 | 45570da5 | \([1, 0, 0, 43955939, 396431270591]\) | \(79834049226144675685439/623263340520316720350\) | \(-73326308748874741832457150\) | \([2]\) | \(15728640\) | \(3.6446\) |