Properties

Label 58800.c
Number of curves $4$
Conductor $58800$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 58800.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.c1 58800gi3 \([0, -1, 0, -369133, -79606988]\) \(189123395584/16078125\) \(472893832031250000\) \([2]\) \(995328\) \(2.1329\)  
58800.c2 58800gi1 \([0, -1, 0, -75133, 7931512]\) \(1594753024/4725\) \(138972881250000\) \([2]\) \(331776\) \(1.5836\) \(\Gamma_0(N)\)-optimal
58800.c3 58800gi2 \([0, -1, 0, -44508, 14424012]\) \(-20720464/178605\) \(-84050798580000000\) \([2]\) \(663552\) \(1.9301\)  
58800.c4 58800gi4 \([0, -1, 0, 396492, -367481988]\) \(14647977776/132355125\) \(-62285792404500000000\) \([2]\) \(1990656\) \(2.4795\)  

Rank

sage: E.rank()
 

The elliptic curves in class 58800.c have rank \(1\).

Complex multiplication

The elliptic curves in class 58800.c do not have complex multiplication.

Modular form 58800.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} - 6q^{11} - 4q^{13} + 6q^{17} + 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.