Properties

Label 90480.i
Number of curves $2$
Conductor $90480$
CM no
Rank $0$
Graph

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

Elliptic curves in class 90480.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
90480.i1 90480y2 \([0, -1, 0, -56381, 66357681]\) \(-77426525890207744/7381623919921875\) \(-1889695723500000000\) \([]\) \(1492992\) \(2.1865\)  
90480.i2 90480y1 \([0, -1, 0, 6259, -2446095]\) \(105908108681216/10141028512875\) \(-2596103299296000\) \([]\) \(497664\) \(1.6372\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 90480.i have rank \(0\).

Complex multiplication

The elliptic curves in class 90480.i do not have complex multiplication.

Modular form 90480.2.a.i

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