Properties

Label 94864.t
Number of curves $2$
Conductor $94864$
CM no
Rank $0$
Graph

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

Elliptic curves in class 94864.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
94864.t1 94864dc2 \([0, 1, 0, -4934904, -4335698732]\) \(-128667913/4096\) \(-423106422088457519104\) \([]\) \(4561920\) \(2.7338\)  
94864.t2 94864dc1 \([0, 1, 0, 282616, -21853196]\) \(24167/16\) \(-1652759461283037184\) \([]\) \(1520640\) \(2.1845\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 94864.t have rank \(0\).

Complex multiplication

The elliptic curves in class 94864.t do not have complex multiplication.

Modular form 94864.2.a.t

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} + 3 q^{5} + q^{9} - 5 q^{13} - 6 q^{15} - 3 q^{17} + 2 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.