Properties

Label 61936n
Number of curves $3$
Conductor $61936$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 61936n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
61936.t3 61936n1 \([0, 1, 0, -36472, 2668756]\) \(11134383337/316\) \(152277336064\) \([]\) \(120960\) \(1.2473\) \(\Gamma_0(N)\)-optimal
61936.t2 61936n2 \([0, 1, 0, -63912, -1886284]\) \(59914169497/31554496\) \(15205805670006784\) \([]\) \(362880\) \(1.7967\)  
61936.t1 61936n3 \([0, 1, 0, -4089752, -3184777324]\) \(15698803397448457/20709376\) \(9979647496290304\) \([]\) \(1088640\) \(2.3460\)  

Rank

sage: E.rank()
 

The elliptic curves in class 61936n have rank \(1\).

Complex multiplication

The elliptic curves in class 61936n do not have complex multiplication.

Modular form 61936.2.a.n

sage: E.q_eigenform(10)
 
\(q + q^{3} - 3 q^{5} - 2 q^{9} - 5 q^{13} - 3 q^{15} + 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.