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Properties

Label 322530.bb
Number of curves $2$
Conductor $322530$
CM no
Rank $1$
Graph

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

Elliptic curves in class 322530.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
322530.bb1 322530bb2 \([1, 0, 0, -32057602950, -2204027200028100]\) \(3643483851824804802367372393822504801/9960778515925329882659257650600\) \(9960778515925329882659257650600\) \([]\) \(929359872\) \(4.8214\)  
322530.bb2 322530bb1 \([1, 0, 0, -1855549950, 30764846002500]\) \(706547983592544968099969232472801/300959193600000000000000\) \(300959193600000000000000\) \([7]\) \(132765696\) \(3.8484\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 322530.bb have rank \(1\).

Complex multiplication

The elliptic curves in class 322530.bb do not have complex multiplication.

Modular form 322530.2.a.bb

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{7} + q^{8} + q^{9} + q^{10} - 2 q^{11} + q^{12} - q^{13} + q^{14} + q^{15} + q^{16} - 3 q^{17} + q^{18} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.