Properties

Label 433200.jp
Number of curves $2$
Conductor $433200$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("jp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 433200.jp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
433200.jp1 433200jp2 \([0, 1, 0, -526485408, -4649899660812]\) \(781484460931/900\) \(18586811392070400000000\) \([2]\) \(84049920\) \(3.5571\) \(\Gamma_0(N)\)-optimal*
433200.jp2 433200jp1 \([0, 1, 0, -32637408, -73904092812]\) \(-186169411/6480\) \(-133825042022906880000000\) \([2]\) \(42024960\) \(3.2105\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 433200.jp1.

Rank

sage: E.rank()
 

The elliptic curves in class 433200.jp have rank \(1\).

Complex multiplication

The elliptic curves in class 433200.jp do not have complex multiplication.

Modular form 433200.2.a.jp

sage: E.q_eigenform(10)
 
\(q + q^{3} + 2 q^{7} + q^{9} - 2 q^{13} + 6 q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.