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Properties

Label 450450.fv
Number of curves $4$
Conductor $450450$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("fv1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 450450.fv have rank \(1\).

Complex multiplication

The elliptic curves in class 450450.fv do not have complex multiplication.

Modular form 450450.2.a.fv

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{7} + q^{8} - q^{11} - q^{13} - q^{14} + q^{16} - 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 450450.fv

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
450450.fv1 450450fv3 \([1, -1, 1, -38855255, 93232644747]\) \(569541582763202518561/828928100\) \(9442009139062500\) \([2]\) \(24883200\) \(2.7651\) \(\Gamma_0(N)\)-optimal*
450450.fv2 450450fv4 \([1, -1, 1, -38844005, 93289322247]\) \(-569047017391330383361/687121794969610\) \(-7826746695825713906250\) \([2]\) \(49766400\) \(3.1116\)  
450450.fv3 450450fv1 \([1, -1, 1, -492755, 120669747]\) \(1161631688686561/121121000000\) \(1379643890625000000\) \([2]\) \(8294400\) \(2.2158\) \(\Gamma_0(N)\)-optimal*
450450.fv4 450450fv2 \([1, -1, 1, 632245, 590919747]\) \(2453765252833439/14670296641000\) \(-167103847676390625000\) \([2]\) \(16588800\) \(2.5623\)  
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 450450.fv1.