Properties

Label 115920.ch
Number of curves $4$
Conductor $115920$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ch1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.ch

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.ch1 115920dv4 \([0, 0, 0, -121147389723, -16230025616545078]\) \(65853432878493908038433301506521/38511703125000000\) \(114995329344000000000000\) \([2]\) \(247726080\) \(4.6502\)  
115920.ch2 115920dv2 \([0, 0, 0, -7571755803, -253591059413302]\) \(16077778198622525072705635801/388799208512064000000\) \(1160948215829686910976000000\) \([2, 2]\) \(123863040\) \(4.3036\)  
115920.ch3 115920dv3 \([0, 0, 0, -7289515803, -273368011349302]\) \(-14346048055032350809895395801/2509530875136386550792000\) \(-7493419040663248058480099328000\) \([2]\) \(247726080\) \(4.6502\)  
115920.ch4 115920dv1 \([0, 0, 0, -490918683, -3650254584118]\) \(4381924769947287308715481/608122186185572352000\) \(1815843117995140073914368000\) \([2]\) \(61931520\) \(3.9570\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 115920.ch have rank \(1\).

Complex multiplication

The elliptic curves in class 115920.ch do not have complex multiplication.

Modular form 115920.2.a.ch

sage: E.q_eigenform(10)
 
\(q - q^{5} + q^{7} + 4q^{11} + 6q^{13} - 2q^{17} + O(q^{20})\)  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.