Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("dn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 119952.dn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119952.dn1 119952s1 \([0, 0, 0, -21315, 1184722]\) \(12194500/153\) \(13437149709312\) \([2]\) \(184320\) \(1.3285\) \(\Gamma_0(N)\)-optimal
119952.dn2 119952s2 \([0, 0, 0, -3675, 3086314]\) \(-31250/23409\) \(-4111767811049472\) \([2]\) \(368640\) \(1.6751\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 119952.2.a.dn

sage: E.q_eigenform(10)
 
\(q - 2q^{13} - q^{17} + 4q^{19} + O(q^{20})\)  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 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.