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Properties

Label 414736j
Number of curves $2$
Conductor $414736$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("j1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 414736j have rank \(1\).

Complex multiplication

The elliptic curves in class 414736j do not have complex multiplication.

Modular form 414736.2.a.j

Copy content sage:E.q_eigenform(10)
 
\(q - 2 q^{3} + 2 q^{5} + q^{9} - 4 q^{11} - 4 q^{15} - 6 q^{17} - 8 q^{19} + O(q^{20})\) 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 414736j

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
414736.j1 414736j1 \([0, 1, 0, -23452, -1111860]\) \(109744/23\) \(298970912850176\) \([2]\) \(1622016\) \(1.4924\) \(\Gamma_0(N)\)-optimal
414736.j2 414736j2 \([0, 1, 0, 50608, -6651548]\) \(275684/529\) \(-27505323982216192\) \([2]\) \(3244032\) \(1.8390\)