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Properties

Label 485184.io
Number of curves $2$
Conductor $485184$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("io1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 485184.io have rank \(1\).

Complex multiplication

The elliptic curves in class 485184.io do not have complex multiplication.

Modular form 485184.2.a.io

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

Isogeny matrix

Copy content 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 485184.io

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
485184.io1 485184io1 \([0, 1, 0, -8179297, -7185475297]\) \(4906933498657/1032471552\) \(12733260436937719676928\) \([2]\) \(33177600\) \(2.9563\) \(\Gamma_0(N)\)-optimal
485184.io2 485184io2 \([0, 1, 0, 17697183, -43428073185]\) \(49702082429663/94844496096\) \(-1169697767905658293714944\) \([2]\) \(66355200\) \(3.3028\)