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Properties

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

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Show commands: SageMath
Copy content sage:E = EllipticCurve("cu1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

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

Complex multiplication

The elliptic curves in class 400752cu do not have complex multiplication.

Modular form 400752.2.a.cu

Copy content sage:E.q_eigenform(10)
 
\(q - 2 q^{7} - 2 q^{13} - 8 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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

Copy content sage:E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.

Elliptic curves in class 400752cu

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
400752.cu2 400752cu1 \([0, 0, 0, 731445, 143319418]\) \(8181353375/6412032\) \(-33918705435455520768\) \([2]\) \(8847360\) \(2.4355\) \(\Gamma_0(N)\)-optimal*
400752.cu1 400752cu2 \([0, 0, 0, -3450315, 1238104186]\) \(858729462625/371764272\) \(1966578275559848214528\) \([2]\) \(17694720\) \(2.7821\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 400752cu1.