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Properties

Label 379050.bb
Number of curves $2$
Conductor $379050$
CM no
Rank $0$
Graph

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

Elliptic curves in class 379050.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
379050.bb1 379050bb1 \([1, 1, 0, -410825, 58220625]\) \(1520875/588\) \(2964693223344562500\) \([2]\) \(8755200\) \(2.2434\) \(\Gamma_0(N)\)-optimal
379050.bb2 379050bb2 \([1, 1, 0, 1303925, 420032875]\) \(48627125/43218\) \(-217904951915825343750\) \([2]\) \(17510400\) \(2.5900\)  

Rank

sage: E.rank()
 

The elliptic curves in class 379050.bb have rank \(0\).

Complex multiplication

The elliptic curves in class 379050.bb do not have complex multiplication.

Modular form 379050.2.a.bb

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.