Properties

Label 119952w
Number of curves $2$
Conductor $119952$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 119952w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119952.fo2 119952w1 \([0, 0, 0, -4179, -134750]\) \(-31522396/12393\) \(-3173204450304\) \([2]\) \(221184\) \(1.1079\) \(\Gamma_0(N)\)-optimal
119952.fo1 119952w2 \([0, 0, 0, -72219, -7469462]\) \(81344187038/7803\) \(3995887085568\) \([2]\) \(442368\) \(1.4545\)  

Rank

sage: E.rank()
 

The elliptic curves in class 119952w have rank \(1\).

Complex multiplication

The elliptic curves in class 119952w do not have complex multiplication.

Modular form 119952.2.a.w

sage: E.q_eigenform(10)
 
\(q + 2 q^{5} - 6 q^{13} - q^{17} - 8 q^{19} + O(q^{20})\)  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.