Properties

Label 96192t
Number of curves $2$
Conductor $96192$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 96192t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
96192.l2 96192t1 \([0, 0, 0, 1140, 35728]\) \(3429500/13527\) \(-646262489088\) \([2]\) \(81920\) \(0.94892\) \(\Gamma_0(N)\)-optimal
96192.l1 96192t2 \([0, 0, 0, -11820, 434896]\) \(1911343250/251001\) \(23983519039488\) \([2]\) \(163840\) \(1.2955\)  

Rank

sage: E.rank()
 

The elliptic curves in class 96192t have rank \(2\).

Complex multiplication

The elliptic curves in class 96192t do not have complex multiplication.

Modular form 96192.2.a.t

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.