Properties

Label 185900.be
Number of curves $2$
Conductor $185900$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 185900.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
185900.be1 185900be1 \([0, -1, 0, -7526133, 7958049137]\) \(-2441851961344/3020875\) \(-58324746551500000000\) \([]\) \(6967296\) \(2.7022\) \(\Gamma_0(N)\)-optimal
185900.be2 185900be2 \([0, -1, 0, 10049867, 36874963137]\) \(5814126903296/33794921875\) \(-652486532242187500000000\) \([]\) \(20901888\) \(3.2515\)  

Rank

sage: E.rank()
 

The elliptic curves in class 185900.be have rank \(1\).

Complex multiplication

The elliptic curves in class 185900.be do not have complex multiplication.

Modular form 185900.2.a.be

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