Properties

Label 377520.br
Number of curves $2$
Conductor $377520$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("br1")
 
E.isogeny_class()
 

Elliptic curves in class 377520.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
377520.br1 377520br2 \([0, -1, 0, -825040, -203609888]\) \(22784591413352662/6597644551875\) \(17984440112221440000\) \([2]\) \(13160448\) \(2.4009\)  
377520.br2 377520br1 \([0, -1, 0, 137240, -21161600]\) \(209741642018356/262704572325\) \(-358051620622924800\) \([2]\) \(6580224\) \(2.0543\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 377520.br have rank \(0\).

Complex multiplication

The elliptic curves in class 377520.br do not have complex multiplication.

Modular form 377520.2.a.br

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - 4 q^{7} + q^{9} - q^{13} - q^{15} - 6 q^{17} + 4 q^{19} + O(q^{20})\) 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 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.