Properties

Label 242550il
Number of curves $2$
Conductor $242550$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("il1")
 
E.isogeny_class()
 

Elliptic curves in class 242550il

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
242550.il1 242550il1 \([1, -1, 1, -230716730, 1348745899897]\) \(37537160298467283/5519360000\) \(199704697426080000000000\) \([2]\) \(49545216\) \(3.4852\) \(\Gamma_0(N)\)-optimal
242550.il2 242550il2 \([1, -1, 1, -209548730, 1606233451897]\) \(-28124139978713043/14526050000000\) \(-525589999573521093750000000\) \([2]\) \(99090432\) \(3.8317\)  

Rank

sage: E.rank()
 

The elliptic curves in class 242550il have rank \(1\).

Complex multiplication

The elliptic curves in class 242550il do not have complex multiplication.

Modular form 242550.2.a.il

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{8} - q^{11} - 4 q^{13} + q^{16} + 2 q^{17} + 6 q^{19} + O(q^{20})\) 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.