Properties

Label 207025bb
Number of curves $2$
Conductor $207025$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bb1")
 
E.isogeny_class()
 

Elliptic curves in class 207025bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
207025.bb2 207025bb1 \([1, 0, 0, -33888, 2611517]\) \(-9317\) \(-461940705078125\) \([]\) \(552960\) \(1.5522\) \(\Gamma_0(N)\)-optimal
207025.bb1 207025bb2 \([1, 0, 0, -879150763, -10033358282858]\) \(-162677523113838677\) \(-461940705078125\) \([]\) \(20459520\) \(3.3577\)  

Rank

sage: E.rank()
 

The elliptic curves in class 207025bb have rank \(1\).

Complex multiplication

The elliptic curves in class 207025bb do not have complex multiplication.

Modular form 207025.2.a.bb

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} - q^{6} + 3 q^{8} - 2 q^{9} - q^{12} - q^{16} - 2 q^{17} + 2 q^{18} + 6 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.