Properties

Label 352800pa
Number of curves $2$
Conductor $352800$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("pa1")
 
E.isogeny_class()
 

Elliptic curves in class 352800pa

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
352800.pa2 352800pa1 \([0, 0, 0, -19425, -24500]\) \(3241792/1875\) \(468838125000000\) \([2]\) \(1572864\) \(1.5046\) \(\Gamma_0(N)\)-optimal
352800.pa1 352800pa2 \([0, 0, 0, -216300, -38612000]\) \(69934528/225\) \(3600676800000000\) \([2]\) \(3145728\) \(1.8512\)  

Rank

sage: E.rank()
 

The elliptic curves in class 352800pa have rank \(1\).

Complex multiplication

The elliptic curves in class 352800pa do not have complex multiplication.

Modular form 352800.2.a.pa

sage: E.q_eigenform(10)
 
\(q + 6 q^{11} + 4 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.