Properties

Label 133952bd
Number of curves $2$
Conductor $133952$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bd1")
 
E.isogeny_class()
 

Elliptic curves in class 133952bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
133952.cb1 133952bd1 \([0, 1, 0, -174749, -28175407]\) \(-9221261135586623488/121324931\) \(-7764795584\) \([]\) \(497664\) \(1.4561\) \(\Gamma_0(N)\)-optimal
133952.cb2 133952bd2 \([0, 1, 0, -164869, -31491551]\) \(-7743965038771437568/2189290237869371\) \(-140114575223639744\) \([]\) \(1492992\) \(2.0054\)  

Rank

sage: E.rank()
 

The elliptic curves in class 133952bd have rank \(1\).

Complex multiplication

The elliptic curves in class 133952bd do not have complex multiplication.

Modular form 133952.2.a.bd

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.