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Properties

Label 478800fn
Number of curves $2$
Conductor $478800$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("fn1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 478800fn have rank \(1\).

Complex multiplication

The elliptic curves in class 478800fn do not have complex multiplication.

Modular form 478800.2.a.fn

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 478800fn

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
478800.fn1 478800fn1 \([0, 0, 0, -1274475, -441787750]\) \(4906933498657/1032471552\) \(48170992730112000000\) \([2]\) \(11796480\) \(2.4915\) \(\Gamma_0(N)\)-optimal
478800.fn2 478800fn2 \([0, 0, 0, 2757525, -2671483750]\) \(49702082429663/94844496096\) \(-4425064809854976000000\) \([2]\) \(23592960\) \(2.8381\)