Properties

Label 142956.s
Number of curves $2$
Conductor $142956$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 142956.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
142956.s1 142956n2 \([0, 0, 0, -183540, -30272947]\) \(-162390710272000/47832147\) \(-201407012701488\) \([]\) \(466560\) \(1.7236\)  
142956.s2 142956n1 \([0, 0, 0, 1140, -151639]\) \(38912000/2381643\) \(-10028393706672\) \([]\) \(155520\) \(1.1743\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 142956.s have rank \(1\).

Complex multiplication

The elliptic curves in class 142956.s do not have complex multiplication.

Modular form 142956.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{7} + q^{11} + q^{13} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.