Properties

Label 435344c
Number of curves $2$
Conductor $435344$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 435344c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
435344.c2 435344c1 \([0, 1, 0, -1260120, 642811924]\) \(-11192824869409/2563305472\) \(-50678111936507281408\) \([2]\) \(20127744\) \(2.5007\) \(\Gamma_0(N)\)-optimal*
435344.c1 435344c2 \([0, 1, 0, -21161560, 37460475924]\) \(53008645999484449/2060047808\) \(40728401101146816512\) \([2]\) \(40255488\) \(2.8473\) \(\Gamma_0(N)\)-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 435344c1.

Rank

sage: E.rank()
 

The elliptic curves in class 435344c have rank \(0\).

Complex multiplication

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

Modular form 435344.2.a.c

sage: E.q_eigenform(10)
 
\(q - 2q^{3} - 4q^{5} - q^{7} + q^{9} - 4q^{11} + 8q^{15} + 8q^{19} + O(q^{20})\)  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 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.