Properties

Label 154800.ft
Number of curves $2$
Conductor $154800$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ft1")
 
E.isogeny_class()
 

Elliptic curves in class 154800.ft

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
154800.ft1 154800em2 \([0, 0, 0, -4500009675, -116189875095750]\) \(8000051600110940079507/144453125\) \(181969335000000000000\) \([2]\) \(82575360\) \(3.8784\)  
154800.ft2 154800em1 \([0, 0, 0, -281259675, -1815343845750]\) \(1953326569433829507/262451171875\) \(330612890625000000000000\) \([2]\) \(41287680\) \(3.5318\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 154800.ft have rank \(0\).

Complex multiplication

The elliptic curves in class 154800.ft do not have complex multiplication.

Modular form 154800.2.a.ft

sage: E.q_eigenform(10)
 
\(q + 4 q^{7} - 4 q^{11} - 2 q^{13} - 6 q^{17} + 6 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.