Properties

Label 78650cn
Number of curves $2$
Conductor $78650$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cn1")
 
E.isogeny_class()
 

Elliptic curves in class 78650cn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
78650.dh2 78650cn1 \([1, 1, 1, -15793, 959311]\) \(-9836106385/3407872\) \(-150931328204800\) \([]\) \(486000\) \(1.4320\) \(\Gamma_0(N)\)-optimal
78650.dh1 78650cn2 \([1, 1, 1, -1370993, 617304271]\) \(-6434774386429585/140608\) \(-6227391227200\) \([]\) \(1458000\) \(1.9813\)  

Rank

sage: E.rank()
 

The elliptic curves in class 78650cn have rank \(0\).

Complex multiplication

The elliptic curves in class 78650cn do not have complex multiplication.

Modular form 78650.2.a.cn

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