Properties

Label 40560.cg
Number of curves $4$
Conductor $40560$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("cg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 40560.cg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40560.cg1 40560t4 \([0, 1, 0, -1406136, -642253260]\) \(31103978031362/195\) \(1927634442240\) \([2]\) \(516096\) \(1.9629\)  
40560.cg2 40560t3 \([0, 1, 0, -121736, -1648620]\) \(20183398562/11567205\) \(114345347479234560\) \([2]\) \(516096\) \(1.9629\)  
40560.cg3 40560t2 \([0, 1, 0, -87936, -10044540]\) \(15214885924/38025\) \(187944358118400\) \([2, 2]\) \(258048\) \(1.6163\)  
40560.cg4 40560t1 \([0, 1, 0, -3436, -276340]\) \(-3631696/24375\) \(-30119288160000\) \([2]\) \(129024\) \(1.2697\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 40560.cg have rank \(0\).

Complex multiplication

The elliptic curves in class 40560.cg do not have complex multiplication.

Modular form 40560.2.a.cg

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + 4q^{7} + q^{9} + 4q^{11} - q^{15} + 6q^{17} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.