Properties

Label 48400.ci
Number of curves $4$
Conductor $48400$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ci1")
 
E.isogeny_class()
 

Elliptic curves in class 48400.ci

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
48400.ci1 48400bx4 \([0, 1, 0, -6075208, -5765686412]\) \(-349938025/8\) \(-566899520000000000\) \([]\) \(972000\) \(2.5200\)  
48400.ci2 48400bx3 \([0, 1, 0, -25208, -18186412]\) \(-25/2\) \(-141724880000000000\) \([]\) \(324000\) \(1.9707\)  
48400.ci3 48400bx1 \([0, 1, 0, -5848, 205588]\) \(-121945/32\) \(-5805051084800\) \([]\) \(64800\) \(1.1660\) \(\Gamma_0(N)\)-optimal
48400.ci4 48400bx2 \([0, 1, 0, 42552, -1517452]\) \(46969655/32768\) \(-5944372310835200\) \([]\) \(194400\) \(1.7153\)  

Rank

sage: E.rank()
 

The elliptic curves in class 48400.ci have rank \(1\).

Complex multiplication

The elliptic curves in class 48400.ci do not have complex multiplication.

Modular form 48400.2.a.ci

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{7} - 2 q^{9} - 4 q^{13} - 3 q^{17} + 5 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 3 & 15 & 5 \\ 3 & 1 & 5 & 15 \\ 15 & 5 & 1 & 3 \\ 5 & 15 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.