Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 435344.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
435344.m1 435344m2 \([0, 1, 0, -37912, 2374932]\) \(304821217/51842\) \(1024947946201088\) \([2]\) \(2488320\) \(1.6009\) \(\Gamma_0(N)\)-optimal*
435344.m2 435344m1 \([0, 1, 0, -10872, -404780]\) \(7189057/644\) \(12732272623616\) \([2]\) \(1244160\) \(1.2544\) \(\Gamma_0(N)\)-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 435344.m1.

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 435344.2.a.m

sage: E.q_eigenform(10)
 
\(q - 2q^{3} + 2q^{5} + q^{7} + q^{9} + 6q^{11} - 4q^{15} - 2q^{17} + 4q^{19} + O(q^{20})\)  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.