Properties

Label 182070.df
Number of curves $8$
Conductor $182070$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("df1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 182070.df

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
182070.df1 182070v7 \([1, -1, 1, -913555787, 10628208252699]\) \(4791901410190533590281/41160000\) \(724263205889160000\) \([2]\) \(42467328\) \(3.4682\)  
182070.df2 182070v6 \([1, -1, 1, -57098507, 166068703131]\) \(1169975873419524361/108425318400\) \(1907883107481460838400\) \([2, 2]\) \(21233664\) \(3.1216\)  
182070.df3 182070v8 \([1, -1, 1, -52936907, 191299651611]\) \(-932348627918877961/358766164249920\) \(-6312952679402429611225920\) \([2]\) \(42467328\) \(3.4682\)  
182070.df4 182070v4 \([1, -1, 1, -11333912, 14431100199]\) \(9150443179640281/184570312500\) \(3247752338270507812500\) \([2]\) \(14155776\) \(2.9189\)  
182070.df5 182070v3 \([1, -1, 1, -3830027, 2193551259]\) \(353108405631241/86318776320\) \(1518890030756863672320\) \([2]\) \(10616832\) \(2.7750\)  
182070.df6 182070v2 \([1, -1, 1, -1502132, -371627769]\) \(21302308926361/8930250000\) \(157139249134880250000\) \([2, 2]\) \(7077888\) \(2.5723\)  
182070.df7 182070v1 \([1, -1, 1, -1294052, -566057721]\) \(13619385906841/6048000\) \(106422348620448000\) \([2]\) \(3538944\) \(2.2257\) \(\Gamma_0(N)\)-optimal
182070.df8 182070v5 \([1, -1, 1, 5000368, -2733335769]\) \(785793873833639/637994920500\) \(-11226342236694114820500\) \([2]\) \(14155776\) \(2.9189\)  

Rank

sage: E.rank()
 

The elliptic curves in class 182070.df have rank \(0\).

Complex multiplication

The elliptic curves in class 182070.df do not have complex multiplication.

Modular form 182070.2.a.df

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} - q^{7} + q^{8} + q^{10} + 2q^{13} - q^{14} + q^{16} + 8q^{19} + O(q^{20})\)  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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.