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Properties

Label 142373c
Number of curves $2$
Conductor $142373$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 142373c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
142373.c2 142373c1 \([1, 0, 0, 6433, -753032]\) \(4657463/41503\) \(-262355530622647\) \([2]\) \(451584\) \(1.4480\) \(\Gamma_0(N)\)-optimal
142373.c1 142373c2 \([1, 0, 0, -95262, -10454735]\) \(15124197817/1294139\) \(8180722454869811\) \([2]\) \(903168\) \(1.7946\)  

Rank

sage: E.rank()
 

The elliptic curves in class 142373c have rank \(0\).

Complex multiplication

The elliptic curves in class 142373c do not have complex multiplication.

Modular form 142373.2.a.c

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.