Properties

Label 394944.ec
Number of curves $2$
Conductor $394944$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ec1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 394944.ec

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
394944.ec1 394944ec1 [0, -1, 0, -7000737, -7070892255] [2] 25804800 \(\Gamma_0(N)\)-optimal
394944.ec2 394944ec2 [0, -1, 0, -2044577, -16893010143] [2] 51609600  

Rank

sage: E.rank()
 

The elliptic curves in class 394944.ec have rank \(1\).

Complex multiplication

The elliptic curves in class 394944.ec do not have complex multiplication.

Modular form 394944.2.a.ec

sage: E.q_eigenform(10)
 
\( q - q^{3} + 2q^{5} + 4q^{7} + q^{9} - 4q^{13} - 2q^{15} + q^{17} - 8q^{19} + O(q^{20}) \)

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.