Properties

Label 18150.i
Number of curves $2$
Conductor $18150$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 18150.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18150.i1 18150f2 \([1, 1, 0, -5864025, 5446705125]\) \(55025549689/192000\) \(77812273803000000000\) \([]\) \(684288\) \(2.6794\)  
18150.i2 18150f1 \([1, 1, 0, -373650, -82102500]\) \(14235529/1080\) \(437694040141875000\) \([]\) \(228096\) \(2.1300\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 18150.i have rank \(0\).

Complex multiplication

The elliptic curves in class 18150.i do not have complex multiplication.

Modular form 18150.2.a.i

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.