Properties

Label 11025v
Number of curves $3$
Conductor $11025$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11025v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11025.bb2 11025v1 \([0, 0, 1, -14700, 761031]\) \(-262144/35\) \(-46903347421875\) \([]\) \(23040\) \(1.3558\) \(\Gamma_0(N)\)-optimal
11025.bb3 11025v2 \([0, 0, 1, 95550, -1940094]\) \(71991296/42875\) \(-57456600591796875\) \([]\) \(69120\) \(1.9051\)  
11025.bb1 11025v3 \([0, 0, 1, -1447950, -701531469]\) \(-250523582464/13671875\) \(-18321620086669921875\) \([]\) \(207360\) \(2.4544\)  

Rank

sage: E.rank()
 

The elliptic curves in class 11025v have rank \(1\).

Complex multiplication

The elliptic curves in class 11025v do not have complex multiplication.

Modular form 11025.2.a.v

sage: E.q_eigenform(10)
 
\(q - 2q^{4} + 3q^{11} + 5q^{13} + 4q^{16} - 3q^{17} - 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.