Properties

Label 435344.ba
Number of curves $2$
Conductor $435344$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 435344.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
435344.ba1 435344ba2 \([0, 0, 0, -56615, -435006]\) \(16241202000/9332687\) \(11532056987080448\) \([2]\) \(1935360\) \(1.7716\)  
435344.ba2 435344ba1 \([0, 0, 0, -37180, 2748447]\) \(73598976000/336973\) \(26024068946512\) \([2]\) \(967680\) \(1.4250\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 435344.ba1.

Rank

sage: E.rank()
 

The elliptic curves in class 435344.ba have rank \(1\).

Complex multiplication

The elliptic curves in class 435344.ba do not have complex multiplication.

Modular form 435344.2.a.ba

sage: E.q_eigenform(10)
 
\(q - q^{7} - 3q^{9} + 6q^{17} - 4q^{19} + O(q^{20})\)  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.