Properties

Label 35904.bc
Number of curves $2$
Conductor $35904$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 35904.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35904.bc1 35904f2 \([0, -1, 0, -78497, -4862175]\) \(204055591784617/78708537864\) \(20632970949820416\) \([2]\) \(258048\) \(1.8295\)  
35904.bc2 35904f1 \([0, -1, 0, -34977, 2475297]\) \(18052771191337/444958272\) \(116643141255168\) \([2]\) \(129024\) \(1.4829\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 35904.bc have rank \(1\).

Complex multiplication

The elliptic curves in class 35904.bc do not have complex multiplication.

Modular form 35904.2.a.bc

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2 q^{5} - 2 q^{7} + q^{9} - q^{11} - 2 q^{15} - q^{17} - 6 q^{19} + O(q^{20})\) 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.