Properties

Label 349140r
Number of curves $2$
Conductor $349140$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 349140r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
349140.r2 349140r1 \([0, -1, 0, -705, -116478]\) \(-16384/2475\) \(-5862221204400\) \([2]\) \(540672\) \(1.1293\) \(\Gamma_0(N)\)-optimal
349140.r1 349140r2 \([0, -1, 0, -40380, -3084168]\) \(192143824/1815\) \(68783395464960\) \([2]\) \(1081344\) \(1.4759\)  

Rank

sage: E.rank()
 

The elliptic curves in class 349140r have rank \(2\).

Complex multiplication

The elliptic curves in class 349140r do not have complex multiplication.

Modular form 349140.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} - q^{11} - 4 q^{13} - q^{15} + 2 q^{17} - 2 q^{19} + O(q^{20})\) Copy content 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.