Properties

Label 4800bw
Number of curves $2$
Conductor $4800$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bw1")
 
E.isogeny_class()
 

Elliptic curves in class 4800bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4800.be1 4800bw1 \([0, -1, 0, -33, 87]\) \(-102400/3\) \(-120000\) \([]\) \(480\) \(-0.24652\) \(\Gamma_0(N)\)-optimal
4800.be2 4800bw2 \([0, -1, 0, 167, -3713]\) \(20480/243\) \(-6075000000\) \([]\) \(2400\) \(0.55819\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4800bw have rank \(1\).

Complex multiplication

The elliptic curves in class 4800bw do not have complex multiplication.

Modular form 4800.2.a.bw

sage: E.q_eigenform(10)
 
\(q - q^{3} + 3 q^{7} + q^{9} + 2 q^{11} - q^{13} + 2 q^{17} - 5 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.