Properties

Label 379050bf
Number of curves $4$
Conductor $379050$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 379050bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
379050.bf3 379050bf1 \([1, 1, 0, -31775, 1363125]\) \(4826809/1680\) \(1234954376250000\) \([2]\) \(2764800\) \(1.5974\) \(\Gamma_0(N)\)-optimal
379050.bf2 379050bf2 \([1, 1, 0, -212275, -36722375]\) \(1439069689/44100\) \(32417552376562500\) \([2, 2]\) \(5529600\) \(1.9439\)  
379050.bf4 379050bf3 \([1, 1, 0, 58475, -123633125]\) \(30080231/9003750\) \(-6618583610214843750\) \([2]\) \(11059200\) \(2.2905\)  
379050.bf1 379050bf4 \([1, 1, 0, -3371025, -2383673625]\) \(5763259856089/5670\) \(4167971019843750\) \([2]\) \(11059200\) \(2.2905\)  

Rank

sage: E.rank()
 

The elliptic curves in class 379050bf have rank \(1\).

Complex multiplication

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

Modular form 379050.2.a.bf

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.