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Properties

Label 349830bb
Number of curves $2$
Conductor $349830$
CM no
Rank $1$
Graph

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

Elliptic curves in class 349830bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
349830.bb2 349830bb1 \([1, -1, 0, 260820, 120917200]\) \(557644990391/2119680000\) \(-7458610775316480000\) \([2]\) \(8257536\) \(2.3041\) \(\Gamma_0(N)\)-optimal
349830.bb1 349830bb2 \([1, -1, 0, -2659500, 1463680336]\) \(591202341974089/79350000000\) \(279212317435350000000\) \([2]\) \(16515072\) \(2.6507\)  

Rank

sage: E.rank()
 

The elliptic curves in class 349830bb have rank \(1\).

Complex multiplication

The elliptic curves in class 349830bb do not have complex multiplication.

Modular form 349830.2.a.bb

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} + 2 q^{7} - q^{8} + q^{10} + 6 q^{11} - 2 q^{14} + q^{16} + 4 q^{19} + O(q^{20})\) 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.