Properties

Label 304704.u
Number of curves $2$
Conductor $304704$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 304704.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
304704.u1 304704u2 \([0, 0, 0, -17374476, -27290094320]\) \(3370318/81\) \(13940328170353942462464\) \([2]\) \(27131904\) \(3.0338\)  
304704.u2 304704u1 \([0, 0, 0, 146004, -1338759344]\) \(4/9\) \(-774462676130774581248\) \([2]\) \(13565952\) \(2.6872\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 304704.u have rank \(0\).

Complex multiplication

The elliptic curves in class 304704.u do not have complex multiplication.

Modular form 304704.2.a.u

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} - 4 q^{7} - 2 q^{11} - 6 q^{13} - 6 q^{19} + O(q^{20})\) 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.