Properties

Label 9282l
Number of curves $2$
Conductor $9282$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 9282l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9282.i1 9282l1 \([1, 0, 1, -13044382, 18132484496]\) \(245467607504992533120574297/1733763438231552\) \(1733763438231552\) \([2]\) \(349440\) \(2.5220\) \(\Gamma_0(N)\)-optimal
9282.i2 9282l2 \([1, 0, 1, -13036062, 18156772240]\) \(-244998212735457942818233177/652408656229361356416\) \(-652408656229361356416\) \([2]\) \(698880\) \(2.8686\)  

Rank

sage: E.rank()
 

The elliptic curves in class 9282l have rank \(0\).

Complex multiplication

The elliptic curves in class 9282l do not have complex multiplication.

Modular form 9282.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - 2 q^{5} - q^{6} + q^{7} - q^{8} + q^{9} + 2 q^{10} - 2 q^{11} + q^{12} + q^{13} - q^{14} - 2 q^{15} + q^{16} - q^{17} - q^{18} + 8 q^{19} + O(q^{20})\) 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.