Properties

Label 4800.bz
Number of curves $8$
Conductor $4800$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4800.bz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4800.bz1 4800cd7 \([0, 1, 0, -3456033, 2471796063]\) \(1114544804970241/405\) \(1658880000000\) \([2]\) \(49152\) \(2.1353\)  
4800.bz2 4800cd5 \([0, 1, 0, -216033, 38556063]\) \(272223782641/164025\) \(671846400000000\) \([2, 2]\) \(24576\) \(1.7887\)  
4800.bz3 4800cd8 \([0, 1, 0, -176033, 53316063]\) \(-147281603041/215233605\) \(-881596846080000000\) \([2]\) \(49152\) \(2.1353\)  
4800.bz4 4800cd3 \([0, 1, 0, -128033, -17675937]\) \(56667352321/15\) \(61440000000\) \([2]\) \(12288\) \(1.4422\)  
4800.bz5 4800cd4 \([0, 1, 0, -16033, 356063]\) \(111284641/50625\) \(207360000000000\) \([2, 2]\) \(12288\) \(1.4422\)  
4800.bz6 4800cd2 \([0, 1, 0, -8033, -275937]\) \(13997521/225\) \(921600000000\) \([2, 2]\) \(6144\) \(1.0956\)  
4800.bz7 4800cd1 \([0, 1, 0, -33, -11937]\) \(-1/15\) \(-61440000000\) \([2]\) \(3072\) \(0.74901\) \(\Gamma_0(N)\)-optimal
4800.bz8 4800cd6 \([0, 1, 0, 55967, 2732063]\) \(4733169839/3515625\) \(-14400000000000000\) \([2]\) \(24576\) \(1.7887\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4800.2.a.bz

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{9} - 4q^{11} - 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.