Properties

Label 435600jp
Number of curves $2$
Conductor $435600$
CM no
Rank $2$
Graph

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

Elliptic curves in class 435600jp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
435600.jp2 435600jp1 \([0, 0, 0, 825, 211750]\) \(16/5\) \(-19405980000000\) \([2]\) \(663552\) \(1.2289\) \(\Gamma_0(N)\)-optimal*
435600.jp1 435600jp2 \([0, 0, 0, -48675, 4023250]\) \(821516/25\) \(388119600000000\) \([2]\) \(1327104\) \(1.5754\) \(\Gamma_0(N)\)-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 435600jp1.

Rank

sage: E.rank()
 

The elliptic curves in class 435600jp have rank \(2\).

Complex multiplication

The elliptic curves in class 435600jp do not have complex multiplication.

Modular form 435600.2.a.jp

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