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Properties

Label 143745.z
Number of curves $2$
Conductor $143745$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 143745.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
143745.z1 143745x2 \([1, 0, 1, -8252552438, -288550797337969]\) \(478269926289903795013/11864752475625\) \(1541963873970171915937498125\) \([2]\) \(171859968\) \(4.3259\)  
143745.z2 143745x1 \([1, 0, 1, -496311813, -4864745230469]\) \(-104033217621345013/18460501171875\) \(-2399158849785932780855859375\) \([2]\) \(85929984\) \(3.9793\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 143745.z have rank \(0\).

Complex multiplication

The elliptic curves in class 143745.z do not have complex multiplication.

Modular form 143745.2.a.z

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + q^{5} + q^{6} - q^{7} - 3 q^{8} + q^{9} + q^{10} - 4 q^{11} - q^{12} + 4 q^{13} - q^{14} + q^{15} - q^{16} + 2 q^{17} + q^{18} - 2 q^{19} + O(q^{20})\) 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.