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Properties

Label 95550jz
Number of curves $3$
Conductor $95550$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("jz1")
 
E.isogeny_class()
 

Elliptic curves in class 95550jz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
95550.kw3 95550jz1 \([1, 0, 0, 16512, -7764408]\) \(270840023/14329224\) \(-26340919912125000\) \([]\) \(1119744\) \(1.8305\) \(\Gamma_0(N)\)-optimal
95550.kw2 95550jz2 \([1, 0, 0, -148863, 211688217]\) \(-198461344537/10417365504\) \(-19149884909064000000\) \([]\) \(3359232\) \(2.3798\)  
95550.kw1 95550jz3 \([1, 0, 0, -31919238, 69409237092]\) \(-1956469094246217097/36641439744\) \(-67356699131904000000\) \([]\) \(10077696\) \(2.9291\)  

Rank

sage: E.rank()
 

The elliptic curves in class 95550jz have rank \(1\).

Complex multiplication

The elliptic curves in class 95550jz do not have complex multiplication.

Modular form 95550.2.a.jz

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} + 3 q^{11} + q^{12} + q^{13} + q^{16} - 3 q^{17} + q^{18} + 7 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.