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Properties

Label 446400.ft
Number of curves $2$
Conductor $446400$
CM no
Rank $1$
Graph

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

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 446400.ft have rank \(1\).

Complex multiplication

The elliptic curves in class 446400.ft do not have complex multiplication.

Modular form 446400.2.a.ft

Copy content sage:E.q_eigenform(10)
 
\(q - 2 q^{7} + 3 q^{11} - q^{13} + 3 q^{17} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 446400.ft

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
446400.ft1 446400ft2 \([0, 0, 0, -20088300, -34671886000]\) \(-300238092661681/171774906\) \(-512917120917504000000\) \([]\) \(21504000\) \(2.9201\)  
446400.ft2 446400ft1 \([0, 0, 0, 215700, 13394000]\) \(371694959/241056\) \(-719789359104000000\) \([]\) \(4300800\) \(2.1154\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 446400.ft1.