Properties

Label 4800.ca
Number of curves $4$
Conductor $4800$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ca1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4800.ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4800.ca1 4800cc3 \([0, 1, 0, -5633, -163137]\) \(38614472/405\) \(207360000000\) \([2]\) \(6144\) \(0.98802\)  
4800.ca2 4800cc2 \([0, 1, 0, -633, 1863]\) \(438976/225\) \(14400000000\) \([2, 2]\) \(3072\) \(0.64145\)  
4800.ca3 4800cc1 \([0, 1, 0, -508, 4238]\) \(14526784/15\) \(15000000\) \([2]\) \(1536\) \(0.29488\) \(\Gamma_0(N)\)-optimal
4800.ca4 4800cc4 \([0, 1, 0, 2367, 16863]\) \(2863288/1875\) \(-960000000000\) \([2]\) \(6144\) \(0.98802\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4800.2.a.ca

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{9} - 4q^{11} + 2q^{13} + 2q^{17} - 8q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.