Properties

Label 50400bi
Number of curves $2$
Conductor $50400$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bi1")
 
E.isogeny_class()
 

Elliptic curves in class 50400bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
50400.do2 50400bi1 \([0, 0, 0, 375, -15500]\) \(8000/147\) \(-107163000000\) \([2]\) \(36864\) \(0.79691\) \(\Gamma_0(N)\)-optimal
50400.do1 50400bi2 \([0, 0, 0, -7500, -236000]\) \(1000000/63\) \(2939328000000\) \([2]\) \(73728\) \(1.1435\)  

Rank

sage: E.rank()
 

The elliptic curves in class 50400bi have rank \(1\).

Complex multiplication

The elliptic curves in class 50400bi do not have complex multiplication.

Modular form 50400.2.a.bi

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.