Properties

Label 4560.bb
Number of curves $4$
Conductor $4560$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4560.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.bb1 4560g3 \([0, 1, 0, -30400, -2050300]\) \(3034301922374404/1425\) \(1459200\) \([2]\) \(4096\) \(0.95645\)  
4560.bb2 4560g4 \([0, 1, 0, -2280, -18972]\) \(1280615525284/601171875\) \(615600000000\) \([4]\) \(4096\) \(0.95645\)  
4560.bb3 4560g2 \([0, 1, 0, -1900, -32500]\) \(2964647793616/2030625\) \(519840000\) \([2, 2]\) \(2048\) \(0.60988\)  
4560.bb4 4560g1 \([0, 1, 0, -95, -732]\) \(-5988775936/9774075\) \(-156385200\) \([2]\) \(1024\) \(0.26330\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4560.bb have rank \(1\).

Complex multiplication

The elliptic curves in class 4560.bb do not have complex multiplication.

Modular form 4560.2.a.bb

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} - 2 q^{13} + q^{15} - 6 q^{17} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.