Properties

Label 243360u
Number of curves $2$
Conductor $243360$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 243360u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
243360.u2 243360u1 \([0, 0, 0, 41067, 10202868]\) \(1259712/8125\) \(-49403162404440000\) \([2]\) \(1548288\) \(1.8850\) \(\Gamma_0(N)\)-optimal
243360.u1 243360u2 \([0, 0, 0, -529308, 134772768]\) \(42144192/4225\) \(1644137244819763200\) \([2]\) \(3096576\) \(2.2316\)  

Rank

sage: E.rank()
 

The elliptic curves in class 243360u have rank \(1\).

Complex multiplication

The elliptic curves in class 243360u do not have complex multiplication.

Modular form 243360.2.a.u

sage: E.q_eigenform(10)
 
\(q - q^{5} - 2 q^{7} + 4 q^{11} + 4 q^{17} - 2 q^{19} + O(q^{20})\) 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.