Properties

Label 400752cv
Number of curves 2
Conductor 400752
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("400752.cv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 400752cv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
400752.cv2 400752cv1 [0, 0, 0, -401115, 1421909962] [2] 9830400 \(\Gamma_0(N)\)-optimal*
400752.cv1 400752cv2 [0, 0, 0, -21571275, 38262222394] [2] 19660800 \(\Gamma_0(N)\)-optimal*
*optimality has not been proved rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 400752cv1.

Rank

sage: E.rank()
 

The elliptic curves in class 400752cv have rank \(1\).

Modular form 400752.2.a.cv

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

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 Cremona 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 Cremona labels.