Properties

Label 182070db
Number of curves $4$
Conductor $182070$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("db1")
 
E.isogeny_class()
 

Elliptic curves in class 182070db

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
182070.a4 182070db1 \([1, -1, 0, 40637970, -33532924460]\) \(421792317902132351/271682182840320\) \(-4780597879662174346936320\) \([2]\) \(41287680\) \(3.4245\) \(\Gamma_0(N)\)-optimal
182070.a3 182070db2 \([1, -1, 0, -172435950, -275627512364]\) \(32224493437735955329/16782725759385600\) \(295313672547405294535065600\) \([2, 2]\) \(82575360\) \(3.7710\)  
182070.a2 182070db3 \([1, -1, 0, -1559081070, 23494520463700]\) \(23818189767728437646209/232359312482640000\) \(4088661335687025256274640000\) \([2]\) \(165150720\) \(4.1176\)  
182070.a1 182070db4 \([1, -1, 0, -2194973550, -39542386001324]\) \(66464620505913166201729/74880071980801920\) \(1317611297133786731093377920\) \([2]\) \(165150720\) \(4.1176\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 182070.2.a.db

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + q^{10} - 4 q^{11} - 6 q^{13} + q^{14} + q^{16} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.