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Properties

Label 486720ps
Number of curves $2$
Conductor $486720$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("ps1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 486720ps have rank \(0\).

Complex multiplication

The elliptic curves in class 486720ps do not have complex multiplication.

Modular form 486720.2.a.ps

Copy content sage:E.q_eigenform(10)
 
\(q + q^{5} + 3 q^{7} + 3 q^{11} + 4 q^{17} + 7 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 486720ps

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
486720.ps2 486720ps1 \([0, 0, 0, -504972, 225083664]\) \(-2609064081/2500000\) \(-13645230243840000000\) \([]\) \(10321920\) \(2.3679\) \(\Gamma_0(N)\)-optimal
486720.ps1 486720ps2 \([0, 0, 0, -44309772, -122714547696]\) \(-1762712152495281/171798691840\) \(-937693082298926487306240\) \([]\) \(72253440\) \(3.3408\)