Properties

Label 203280.l
Number of curves $2$
Conductor $203280$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 203280.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
203280.l1 203280em2 \([0, -1, 0, -74588136, -247879996560]\) \(8417729709220226489459/1518688316880000\) \(8279548517446778880000\) \([2]\) \(23224320\) \(3.2094\)  
203280.l2 203280em1 \([0, -1, 0, -4188136, -4690236560]\) \(-1490212288072889459/881798400000000\) \(-4807367353958400000000\) \([2]\) \(11612160\) \(2.8628\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 203280.l have rank \(0\).

Complex multiplication

The elliptic curves in class 203280.l do not have complex multiplication.

Modular form 203280.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - q^{7} + q^{9} - 2 q^{13} + q^{15} + 4 q^{17} - 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.