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Properties

Label 203522f
Number of curves $2$
Conductor $203522$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 203522f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
203522.o2 203522f1 \([1, 0, 0, 506685, -230533951]\) \(13651919/29696\) \(-31292629118820709376\) \([]\) \(4536000\) \(2.4250\) \(\Gamma_0(N)\)-optimal
203522.o1 203522f2 \([1, 0, 0, -46303375, 122092293709]\) \(-10418796526321/82044596\) \(-86455789124174336516276\) \([]\) \(22680000\) \(3.2298\)  

Rank

sage: E.rank()
 

The elliptic curves in class 203522f have rank \(1\).

Complex multiplication

The elliptic curves in class 203522f do not have complex multiplication.

Modular form 203522.2.a.f

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + 2 q^{7} + q^{8} - 2 q^{9} + q^{10} + q^{12} + q^{13} + 2 q^{14} + q^{15} + q^{16} + 8 q^{17} - 2 q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.