Properties

Label 176400fn
Number of curves $8$
Conductor $176400$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("fn1")
 
E.isogeny_class()
 

Elliptic curves in class 176400fn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
176400.lp7 176400fn1 \([0, 0, 0, -87762675, -316334236750]\) \(13619385906841/6048000\) \(33197663987712000000000\) \([2]\) \(21233664\) \(3.2799\) \(\Gamma_0(N)\)-optimal
176400.lp6 176400fn2 \([0, 0, 0, -101874675, -207770620750]\) \(21302308926361/8930250000\) \(49018425731856000000000000\) \([2, 2]\) \(42467328\) \(3.6265\)  
176400.lp5 176400fn3 \([0, 0, 0, -259752675, 1224603553250]\) \(353108405631241/86318776320\) \(473806503323715502080000000\) \([2]\) \(63700992\) \(3.8292\)  
176400.lp4 176400fn4 \([0, 0, 0, -768666675, 8058449803250]\) \(9150443179640281/184570312500\) \(1013112304312500000000000000\) \([2]\) \(84934656\) \(3.9731\)  
176400.lp8 176400fn5 \([0, 0, 0, 339125325, -1525919620750]\) \(785793873833639/637994920500\) \(-3501974371135256352000000000\) \([2]\) \(84934656\) \(3.9731\)  
176400.lp2 176400fn6 \([0, 0, 0, -3872424675, 92744423329250]\) \(1169975873419524361/108425318400\) \(595150014550907289600000000\) \([2, 2]\) \(127401984\) \(4.1758\)  
176400.lp1 176400fn7 \([0, 0, 0, -61957416675, 5935920363553250]\) \(4791901410190533590281/41160000\) \(225928546583040000000000\) \([2]\) \(254803968\) \(4.5224\)  
176400.lp3 176400fn8 \([0, 0, 0, -3590184675, 106836948769250]\) \(-932348627918877961/358766164249920\) \(-1969278864240928829460480000000\) \([2]\) \(254803968\) \(4.5224\)  

Rank

sage: E.rank()
 

The elliptic curves in class 176400fn have rank \(0\).

Complex multiplication

The elliptic curves in class 176400fn do not have complex multiplication.

Modular form 176400.2.a.fn

sage: E.q_eigenform(10)
 
\(q + 2 q^{13} + 6 q^{17} + 8 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().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 Cremona numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.